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Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique

The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.

Eidson, T. M.↗

Comparison of AGE and Spectral Methods for the Simulation of Far-Wakes

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This report demonstrates that a good compromise is possible with the Advected Grid Explicit (AGE) method. AGE has proven to be both efficient and accurate for simulating turbulent free-shear flows, including planar mixing layers and planar jets. Its efficiency results from its localized fully explicit finite difference formulation (Bisset 1998a,b) that is very straightforward to compute, outweighing the need for a fairly small timestep. Also, most of the successful simulations were slightly under-resolved, and therefore they were, in effect, large-eddy simulations (LES) without a sub-grid-scale (SGS) model, rather than direct numerical simulations (DNS). The principle is that the role of the smallest scales of turbulent motion (when the Reynolds number is not too low) is to dissipate turbulent energy, and therefore they do not have to be simulated when the numerical method is inherently dissipative at its resolution limits. Such simulations are termed 'auto-LES' (LES with automatic SGS modeling) in this report.

Bisset, D. K.↗

Laboratory for Atmospheres 2008 Technical Highlights

The 2008 Technical Highlights describes the efforts of all members of the Laboratory for Atmospheres. Their dedication to advancing Earth Science through conducting research, developing and running models, designing instruments, managing projects, running field campaigns, and numerous other activities, is highlighted in this report. The Laboratory for Atmospheres (Code 613) is part of the Earth Sciences Division (Code 610), formerly the Earth Sun Exploration Division, under the Sciences and Exploration Directorate (Code 600) based at NASA s Goddard Space Flight Center in Greenbelt, Maryland. In line with NASA s Exploration Initiative, the Laboratory executes a comprehensive research and technology development program dedicated to advancing knowledge and understanding of the atmospheres of Earth and other planets. The research program is aimed at understanding the influence of solar variability on the Earth s climate; predicting the weather and climate of Earth; understanding the structure, dynamics, and radiative properties of precipitation, clouds, and aerosols; understanding atmospheric chemistry, especially the role of natural and anthropogenic trace species on the ozone balance in the stratosphere and the troposphere; and advancing our understanding of physical properties of Earth s atmosphere. The research program identifies problems and requirements for atmospheric observations via satellite missions. Laboratory scientists conceive, design, develop, and implement ultraviolet, infrared, optical, radar, laser, and lidar technology for remote sensing of the atmosphere. Laboratory members conduct field measurements for satellite data calibration and validation, and carry out numerous modeling activities. These modeling activities include climate model simulations, modeling the chemistry and transport of trace species on regional-to-global scales, cloud-resolving models, and development of next-generation Earth system models. Interdisciplinary research is carried out in collaboration with other laboratories and research groups within the Earth Sciences Division, across the Sciences and Exploration Directorate, and with partners in universities and other Government agencies. The Laboratory for Atmospheres is a vital participant in NASA s research agenda. Our Laboratory often has relatively large programs, sizable satellite missions, and observational campaigns that require the cooperative and collaborative efforts of many scientists. We ensure an appropriate balance between our scientists responsibility for these large collaborative projects and their need for an active individual research agenda. This balance allows members of the Laboratory to continuously improve their scientific credentials. Members of the Laboratory interact with the general public to support a wide range of interests in the atmospheric sciences. Among other activities, the Laboratory raises the public s awareness of atmospheric science by presenting public lectures and demonstrations, by making scientific data available to wide audiences, by teaching, and by mentoring students and teachers. The Laboratory makes substantial efforts to attract new scientists to the various areas of atmospheric research. We strongly encourage the establishment of partnerships with Federal and state agencies that have operational responsibilities to promote the societal application of our science products. This report describes our role in NASA s mission, gives a broad description of our research, and summarizes our scientists major accomplishments during calendar year 2008. The report also contains useful information on human resources, scientific interactions, and outreach activities.

Cote, Charles E.↗

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗

Dynamic Smagorinsky Modeled Large-Eddy Simulations of Turbulence Using Tetrahedral Meshes

Eddy-resolving numerical computations of turbulent flows are emerging as viable alternatives to Reynolds Averaged Navier-Stokes (RANS) calculations for flows with an intrinsically steady mean state due to the advances in large-scale parallel computing. In these computations, medium to large turbulent eddies are resolved by the numerics while the smaller or subgrid scales are either modeled or taken care of by the inherent numerical dissipation. To advance the state of the art of unstructured-mesh turbulence simulation capabilities, large eddy simulations (LES) using the dynamic Smagorinsky model (DSM) on tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method. In contrast to what has been reported in the literature, the present implementation of dynamic models allows for active backscattering without any ad-hoc limiting of the eddy viscosity calculated from the subgrid-scale model. For the benchmark problems involving compressible isotropic turbulence decay as well as the shock/turbulent boundary layer interaction benchmark problems, no numerical instability associated with kinetic energy growth is observed and the volume percentage of the backscattering portion accounts for about 38-40% of the simulation domain. A slip-wall model in conjunction with the implemented DSM is used to simulate a relatively high Reynolds number Mach 2.85 turbulent boundary layer over a 30° ramp with several tetrahedral meshes and a wall-normal spacing of either Δγ& = 10 or Δγ& = 20. The computed mean wall pressure distribution, separation region size, mean velocity profiles, and Reynolds stress agree reasonably well with experimental data.

CESE method↗

A Coupled GCM-Cloud Resolving Modeling System, and A Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CFWs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1 998 and 1999). In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a superparameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (2ICE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generatio11 regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

A Coupled GCM-Cloud Resolving Modeling System, and A Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1 998 and 1999).

Tao, Wei-Kuo↗

Precipitation Processes developed during ARM (1997), TOGA COARE(1992), GATE(1 974), SCSMEX(1998) and KWAJEX(1999): Consistent 2D and 3D Cloud Resolving Model Simulations

Real clouds and clouds systems are inherently three dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical cloud system with large horizontal domains at the National Center for Atmospheric Research. The results indicate that surface precipitation and latent heating profiles are very similar between the 2D and 3D simulations of these same cases. The reason for the strong similarity between the 2D and 3D CRM simulations is that the observed large-scale advective tendencies of potential temperature, water vapor mixing ratio, and horizontal momentum were used as the main forcing in both the 2D and 3D models. Interestingly, the 2D and 3D versions of the CRM used in CSU and U.K. Met Office showed significant differences in the rainfall and cloud statistics for three ARM cases. The major objectives of this project are to calculate and axamine: (1)the surface energy and water budgets, (2) the precipitation processes in the convective and stratiform regions, (3) the cloud upward and downward mass fluxes in the convective and stratiform regions; (4) cloud characteristics such as size, updraft intensity and lifetime, and (5) the entrainment and detrainment rates associated with clouds and cloud systems that developed in TOGA COARE, GATE, SCSMEX, ARM and KWAJEX. Of special note is that the analyzed (model generated) data sets are all produced by the same current version of the GCE model, i.e. consistent model physics and configurations. Trajectory analyse and inert tracer calculation will be conducted to identify the differences and similarities in the organization of convection between simulated 2D and 3D cloud systems.

Tao, W.-K.↗

Estimating Resolution Lengths of Hybrid Turbulence Models

A two-stage procedure has been devised for estimating the spatial resolution achievable in the simulation of a given flow on a given computational grid by a computational fluid dynamics (CFD) code that incorporates a hybrid model of turbulence. The hybrid models to which this procedure is especially relevant are those of the Reynolds-averaged Navier-Stokes (RANS) and the partial-averaged Navier-Stokes (PANS) approaches. This procedure represents the first step toward adding variable-resolution turbulence-modeling capabilities to CFD codes as part of a continuing effort to increase the accuracy and robustness of CFD simulations of unsteady flows. Some background information is prerequisite to a meaningful summary of the procedure. Among experts in CFD, it is well known that combination of the Reynolds-averaged Navier-Stokes (RANS) approach and eddy-viscosity turbulence models offers limited capability for simulating unsteady and complex flows. The RANS approach includes an assumption that most of the energy in a given flow is modeled through turbulence-transport equations and is resolved in a computational grid used to simulate the flow. RANS also overpredicts eddy viscosity, thereby yielding excessive damping of unsteady motion. The eddy viscosity attains an unphysically large value because of unresolved scales, and suppresses most temporal and spatial fluctuations in the resolved flow field. One approach used to overcome this deficiency is to provide a mechanism for the RANS equations to resolve motion only on the largest scales and to use a hybrid model to represent effects at smaller scales. The RANS approach involves the use of a standard two-equation turbulence model in which the effect of turbulence is summarized by a viscosity that is a function of (1) the time-averaged kinetic- energy density (k) associated with the local fluctuating (turbulent) component of flow and (2) the time-averaged rate of dissipation of the turbulent-kinetic- energy density ( ). In PANS, which was developed to overcome the grid dependency associated with other hybrid turbulence models (including that of RANS), the standard two-equation turbulence model is replaced by another two-equation model in which one solves for the previously unresolved k and , which are now allowed to vary in space and time.

Abdol-Hamid, Khaled S.↗

Quantifying the Role of Ocean Dynamics in SST Variability across GCMs and Observations

Abstract Midlatitude SSTs forced by mesoscale oceanic processes can affect the large-scale atmosphere, pointing to the ocean’s crucial role outside the tropics. Previous studies have shown oceanic mesoscale processes’ effect on global and regional climate variability. This study quantifies the local contribution of ocean dynamics to mixed-layer temperature across the globe by directly estimating the ocean heat flux divergence resolved by state-of-the-art ocean reanalysis, eddy-resolving, and eddy-parameterized versions of two U.S. national climate models and indirectly from air–sea flux satellite-based estimates. Our results show that the eddy-resolving climate simulations resolve mixed-layer temperature variances that are larger and closer to those inferred from observations than both their eddy-parameterized counterparts and ECCO over much of the extratropics. The observations and the eddy-resolving models indicate a more significant role of ocean dynamics in the mixed-layer temperature variability than the surface fluxes over most extratropics compared to their eddy-parameterized versions. A frequency domain analysis shows that the better-resolved ocean mesoscale and thermal gradients enhance the variance over a time scale from 2 months to 30 years. Results show agreement in the ocean’s contribution among satellite-based estimates, ocean reanalysis products, and ocean eddy-resolving simulations. At the same time, differences emerge for ECCO and the eddy-parameterized models, suggesting that surface fluxes account for a larger fraction of the mixed-layer temperature variability in most of the extratropics.

Siqueira, L.↗

Large-eddy simulation of flow past a circular cylinder

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Mittal, R.↗

Precipitation Processes developed during ARM (1997), TOGA COARE (1992), GATE (1974), SCSMEX (1998), and KWAJEX (1999), Consistent 2D, semi-3D and 3D Cloud Resolving Model Simulations

Real clouds and cloud systems are inherently three-dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. The major objectives of this paper are: (1) to assess the performance of the super-parameterization technique (i.e. is 2D or semi-3D CRM appropriate for the super-parameterization?); (2) calculate and examine the surface energy (especially radiation) and water budgets; (3) identify the differences and similarities in the organization and entrainment rates of convection between simulated 2D and 3D cloud systems.

Tao, Wei-Kuo↗

Precipitation Processes Developed During ARM (1997), TOGA COARE (1992), GATE (1974), SCSMEX (1998), and KWAJEX (1999): Consistent 2D, Semi-3D and 3D Cloud Resolving Model Simulations

Real clouds and cloud systems are inherently three-dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical cloud systems with large horizontal domains at the National Center for Atmospheric Research (NACAR) and at NASA Goddard Space Flight Center . At Goddard, a 3D Goddard Cumulus Ensemble (GCE) model was used to simulate periods during TOGA COARE, SCSMEX and KWAJEX using 512 by 512 km domain (with 2 km resolution). The results indicate that surface precipitation and latent heating profiles are very similar between the 2D and 3D GCE model simulations. The reason for the strong similarity between the 2D and 3D CRM simulations is that the same observed large-scale advective tendencies of potential temperature, water vapor mixing ratio, and horizontal momentum were used as the main focusing in both the 2D and 3D models. Interestingly, the 2D and 3D versions of the CRM used at CSU showed significant differences in the rainfall and cloud statistics for three ARM cases. The major objectives of this paper are: (1) to assess the performance of the super-parameterization technique, (2) calculate and examine the surface energy (especially radiation) and water budgets, and (3) identify the differences and similarities in the organization and entrainment rates of convection between simulated 2D and 3D cloud systems.

Tao, W-K.↗

Precipitation processes developed during TOGA COARE (1992), GATE (1974), SCSMEX (1998), and KWAJEX (1999): 3D Cloud Resolving Model Simulation

Real clouds and cloud systems are inherently three-dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical cloud systems with large horizontal domains at the National Center for Atmospheric Research (NCAR), NOAA GFDL, the U.K. Met. Office, Colorado State University and NASA Goddard Space Flight Center. An improved 3D Goddard Cumulus Ensemble (GCE) model was recently used to simulate periods during TOGA COARE (December 19-27, 1992), GATE (september 1-7, 1974), SCSMEX (May 18-26, June 2-11, 1998) and KWAJEX (August 7-13, August 18-21, and August 29-September 12, 1999) using a 512 by 512 km domain and 41 vertical layers. The major objectives of this paper are: (1) to identify the differences and similarities in the simulated precipitation processes and their associated surface and water energy budgets in TOGA COARE, GATE, KWAJEX, and SCSMEX, and (2) to asses the impact of microphysics, radiation budget and surface fluxes on the organization of convection in tropics.

Tao, W.-K.↗

A coarse-grained model of clay colloidal aggregation and consolidation with explicit representation of the electrical double layer

The aggregation of clay minerals in liquid water exemplifies colloidal self-assembly in nature. These negatively charged aluminosilicate platelets interact through multiple mechanisms with different sensitivities to particle shape, surface charge, aqueous chemistry, and interparticle distance and exhibit complex aggregation structures. Experiments have difficulty resolving the associated colloidal assemblages at the scale of individual particles. Conversely, all-atom molecular dynamics (MD) simulations provide detailed insight on clay colloidal interaction mechanisms, but they are limited to systems containing a few particles. We develop a new coarse-grained (CG) model capable of representing assemblages of hundreds of clay particles with accuracy approaching that of MD simulations, at a fraction of the computational cost. Our CG model is parameterized based on MD simulations of a pair of smectite clay particles in liquid water. A distinctive feature of our model is that it explicitly represents the electrical double layer (EDL), i.e., the cloud of charge-compensating cations that surrounds the clay particles. Our model captures the simultaneous importance of long-range colloidal interactions (i.e., interactions consistent with simplified analytical models, already included in extant clay CG models) and short-range interactions such as ion correlation and surface and ion hydration effects. The resulting simulations correctly predict, at low solid-water ratios, the existence of ordered arrangements of parallel particles separated by water films with a thickness up to ~10 nm and, at high solid-water ratios, the coexistence of crystalline and osmotic swelling states, in agreement with experimental observations.

54 ENVIRONMENTAL SCIENCES↗

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗