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At least 19 records

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗

Performance results of cooperating expert systems in a distributed real-time monitoring system

There are numerous definitions for real-time systems, the most stringent of which involve guaranteeing correct system response within a domain-dependent or situationally defined period of time. For applications such as diagnosis, in which the time required to produce a solution can be non-deterministic, this requirement poses a unique set of challenges in dynamic modification of solution strategy that conforms with maximum possible latencies. However, another definition of real time is relevant in the case of monitoring systems where failure to supply a response in the proper (and often infinitesimal) amount of time allowed does not make the solution less useful (or, in the extreme example of a monitoring system responsible for detecting and deflecting enemy missiles, completely irrelevant). This more casual definition involves responding to data at the same rate at which it is produced, and is more appropriate for monitoring applications with softer real-time constraints, such as interplanetary exploration, which results in massive quantities of data transmitted at the speed of light for a number of hours before it even reaches the monitoring system. The latter definition of real time has been applied to the MARVEL system for automated monitoring and diagnosis of spacecraft telemetry. An early version of this system has been in continuous operational use since it was first deployed in 1989 for the Voyager encounter with Neptune. This system remained under incremental development until 1991 and has been under routine maintenance in operations since then, while continuing to serve as an artificial intelligence (AI) testbed in the laboratory. The system architecture has been designed to facilitate concurrent and cooperative processing by multiple diagnostic expert systems in a hierarchical organization. The diagnostic modules adhere to concepts of data-driven reasoning, constrained but complete nonoverlapping domains, metaknowledge of global consequences of anomalous data, hierarchical reporting of problems that extend beyond a single domain, and shared responsibility for problems that overlap domains. The system enables efficient diagnosis of complex system failures in real-time environments with high data volumes and moderate failure rates, as indicated by extensive performance measurements.

Schwuttke, U. M.↗

Generation of Tollmien-Schlichting waves by free-stream disturbances at low Mach numbers

The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free stream disturbances incident on a flat plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld equation and an appropriate asymptotic solution of the unsteady boundary layer equation match, in the matched asymptotic expansion sense. The analysis leads to a set of scaling laws for the asymptotic structure of the unsteady boundary layer.

Goldstein, M. E.↗

The evolution of Tollmien-Schlichting waves near a leading edge

The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free-stream disturbances incident on a flat-plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary-layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld equation and appropriate asymptotic solutions of the unsteady boundary-layer equation match, in the matched-asymptotic-expansion sense. The analysis explains how long-wavelength free-stream disturbances can generate Tollmien-Schlichting waves of much shorter wavelength. It also leads to a set of scaling laws for the asymptotic structure of the unsteady boundary layer.

Goldstein, M. E.↗

RIACS

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Oliger, Joseph↗

Relation Between Type II Bursts and CMEs Inferred from STEREO Observations

The inner coronagraph (COR1) of the Solar Terrestrial Relations Observatory (STEREO) mission has made it possible to observe coronal mass ejections (CMEs) a in the spatial domain overlapping with that of the metric type II radio bursts. The type II bursts were associated with generally weak flares (mostly B and C class soft X-ray flares), but the CMEs were quite energetic. Using CME data for a set of type II bursts during the declining phase of solar cycle 23, we determine the CME height when the type II bursts start, thus giving an estimate of the heliocentric distance at which CME-driven shocks form. This distance has been determined to be approximately 1.5Rs (solar radii), which coincides with the distance at which the Alfv?n speed profile has a minimum value. We also use type II radio observations from STEREO/WAVES and Wind/WAVES observations to show that CMEs with moderate speed drive either weak shocks or no shock at all when they attain a height where the Alfv?n speed peaks (?3Rs ? 4Rs). Thus the shocks seem to be most efficient in accelerating electrons in the heliocentric distance range of 1.5Rs to 4Rs. By combining the radial variation of the CME speed in the inner corona (CME speed increase) and interplanetary medium (speed decrease) we were able to correctly account for the deviations from the universal drift-rate spectrum of type II bursts, thus confirming the close physical connection between type II bursts and CMEs. The average height (approximately 1.5 Rs) of STEREO CMEs at the time of type II bursts is smaller than that (2.2 Rs) obtained for SOHO (Solar and Heliospheric Observatory) CMEs. We suggest that this may indicate, at least partly, the density reduction in the corona between the maximum and declining phases, so a given plasma level occurs closer to the Sun in the latter phase. In two cases, there was a diffuse shock-like feature ahead of the main body of the CME, indicating a standoff distance of 1Rs - 2Rs by the time the CME left the LASCO field of view.

Gopalswamy, N.↗

Relation Between Type II Bursts and CMEs Inferred from STEREO Observations

The inner coronagraph (COR1) of the Solar Terrestrial Relations Observatory (STEREO) mission has made it possible to observe CMEs in the spatial domain overlapping with that of the metric type II radio bursts. The type II bursts were associated with generally weak flares (mostly B and C class soft X-ray flares), but the CMEs were quite energetic. Using CME data for a set of type II bursts during the declining phase of solar cycle 23, we determine the CME height when the type II bursts start, thus giving an estimate of the heliocentric distance at which CME-driven shocks form. This distance has been determined to be approx. 1.5Rs (solar radii), which coincides with the distance at which the Alfven speed profile has a minimum value.We also use type II radio observations from STEREO/WAVES and Wind/WAVES observations to show that CMEs with moderate speed drive either weak shocks or no shock at all when they attain a height where the Alfven speed peaks (approx. 3Rs - 4Rs). Thus the shocks seem to be most efficient in accelerating electrons in the heliocentric distance range of 1.5Rs to 4Rs. By combining the radial variation of the CME speed in the inner corona (CME speed increase) and interplanetary medium (speed decrease) we were able to correctly account for the deviations from the universal drift-rate spectrum of type II bursts, thus confirming the close physical connection between type II bursts and CMEs. The average height (approx 1.5Rs) of STEREO CMEs at the time of type II bursts is smaller than that (2.2Rs) obtained for SOHO (Solar and Heliospheric Observatory) CMEs. We suggest that this may indicate, at least partly, the density reduction in the corona between the maximum and declining phases, so a given plasma level occurs closer to the Sun in the latter phase. In two cases, there was a diffuse shock-like feature ahead of the main body of the CME, indicating a standoff distance of 1Rs - 2Rs by the time the CME left the LASCO field of view.

Solar Energetic Particles↗

Newton-Krylov-Schwarz: An implicit solver for CFD

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Cai, Xiao-Chuan↗

HEAO 1 observations of active coronae in main-sequence and subgiant stars

The HEAO 1 data has been searched for evidence of X-ray emission from 105 bright late-type stars of luminosity classes IV and V, selected on the basis of indirect optical evidence of the presence of a hot corona. Six of the target stars were detected at the 3-standard deviation level and 15 were coincident with 2-standard deviation X-ray sources. On a statistical basis no more than 5 of these 21 sources are spurious, and the probability that the identification with the class of active chromosphere stars is spurious is less than 0.00001. The sources lie near a line of X-ray/bolometric luminosity ratio = 0.0001, similar to a solar plage, and it is concluded that the most active coronae of late-type stars which are not members of close binary systems are being observed. The RS CVn systems discovered to date seem to form a distinct class of coronal X-ray sources, but the lowest X-ray luminosity members of the group, of which Capella may be the prototype, appear to overlap the domain of these single stars with active coronae. The data do not fit the coronal model of Gorenstein and Tucker (1976), but they are consistent with the coronal loop model of Rosner et al. (1978) as extended by Walter et al. (1980).

Walter, F. M.↗

Challenges in Achieving Trajectory-Based Operations

In the past few years much of the global ATM research community has proposed advanced systems based on Trajectory-Based Operations (TBO). The concept of TBO uses four-dimensional aircraft trajectories as the base information for managing safety and capacity. Both the US and European advanced ATM programs call for the sharing of trajectory data across different decision support tools for successful operations. However, the actual integration of TBO systems presents many challenges. Trajectory predictors are built to meet the specific needs of a particular system and are not always compatible with others. Two case studies are presented which examine the challenges of introducing a new concept into two legacy systems in regards to their trajectory prediction software. The first case describes the issues with integrating a new decision support tool with a legacy operational system which overlap in domain space. These tools perform similar functions but are driven by different requirements. The difference in the resulting trajectories can lead to conflicting advisories. The second case looks at integrating this same new tool with a legacy system originally developed as an integrated system, but diverged many years ago. Both cases illustrate how the lack of common architecture concepts for the trajectory predictors added cost and complexity to the integration efforts.

Cate, Karen Tung↗

A multidomain global modeling technique for analysis of Space Shuttle main engine

A multidomain global modeling technique is presented. The purpose of this multidomain methodology is to simultaneously analyze the three-dimensional compressible flow field in Space Shuttle main engine components. This technique provides flexibility and modularity for individual domain and also simplifies the grid generation task for each domain. A two-way coupling procedure is adopted for exchanging interface boundary conditions. This algorithm which requires that the adjacent domains share an overlapping grid slab, is fully conservative and implicit. For non-matching grid systems and for non-overlapping interfaces, an interpolation and/or extrapolation procedure is used when transferring the interface boundary conditions at the adjacent domains. To maintain overall conservation, a flux correction method is subsequently used. The coupling procedure was verified by modeling several geometries with features similar to SSME components. Satisfactory results for all test cases were obtained. Finally, this algorithm has been applied to the SSME flow simulation.

Tam, L. T.↗

Relationship between radiation-induced aberrations in individual chromosomes and their DNA content: effects of interaction distance

PURPOSE: To study the effect of the interaction distance on the frequency of inter- and intrachromosome exchanges in individual chromosomes with respect to their DNA content. Assumptions: Chromosome exchanges are formed by misrejoining of two DNA double-strand breaks (DSB) induced within an interaction distance, d. It is assumed that chromosomes in G(0)/G(1) phase of the cell cycle occupy a spherical domain in a cell nucleus, with no spatial overlap between individual chromosome domains. RESULTS: Formulae are derived for the probability of formation of inter-, as well as intra-, chromosome exchanges relating to the DNA content of the chromosome for a given interaction distance. For interaction distances <1 microm, the relative frequency of interchromosome exchanges predicted by the present model is similar to that by Cigarran et al. (1998) based on the assumption that the probability of interchromosome exchanges is proportional to the "surface area" of the chromosome territory. The "surface area" assumption is shown to be a limiting case of d-->0 in the present model. The present model also predicts that the probability of intrachromosome exchanges occurring in individual chromosomes is proportional to their DNA content with correction terms. CONCLUSION: When the interaction distance is small, the "surface area" distribution for chromosome participation in interchromosome exchanges has been expected. However, the present model shows that for the interaction distance as large as 1 microm, the predicted probability of interchromosome exchange formation is still close to the surface area distribution. Therefore, this distribution does not necessarily rule out the formation of complex chromosomal aberrations by long-range misrejoining of DSB.

Non-programmatic↗

Functional domains of plant chimeric calcium/calmodulin-dependent protein kinase: regulation by autoinhibitory and visinin-like domains

A novel calcium-binding calcium/calmodulin-dependent protein kinase (CCaMK) with a catalytic domain, calmodulin-binding domain, and a neural visinin-like domain was cloned and characterized from plants [Patil et al., (1995) Proc. Natl. Acad. Sci. USA 92, 4797-4801; Takezawa et al. (1996) J. Biol. Chem. 271, 8126-8132]. The mechanisms of CCaMK activation by calcium and calcium/calmodulin were investigated using various deletion mutants. The use of deletion mutants of CCaMK lacking either one, two, or all three calcium-binding EF hands indicated that all three calcium-binding sites in the visinin-like domain were crucial for the full calcium/calmodulin-dependent kinase activity. As each calcium-binding EF hand was deleted, there was a gradual reduction in calcium/calmodulin-dependent kinase activity from 100 to 4%. Another mutant (amino acids 1-322) which lacks both the visinin-like domain containing three EF hands and the calmodulin-binding domain was constitutively active, indicating the presence of an autoinhibitory domain around the calmodulin-binding domain. By using various synthetic peptides and the constitutively active mutant, we have shown that CCaMK contains an autoinhibitory domain within the residues 322-340 which overlaps its calmodulin-binding domain. Kinetic studies with both ATP and the GS peptide substrate suggest that the autoinhibitory domain of CCaMK interacts only with the peptide substrate binding motif of the catalytic domain, but not with the ATP-binding motif.

Non-NASA Center↗

Thermodynamic constraints on the textural evolution of eucrite, EET 90020

Basaltic eucrites, which are possibly parts of the Vestan crust, formed as either lava flows or intrusions, and can offer insights into early crust formation. However most eucrites have experienced thermal metamorphism, which exacerbates the challenges of understanding these samples. A variety of petrogenetic models such as, partial melting of a primitive source, fractional crystallization of magmas emplaced in a primitive crust, and/or partial melting of a eucritic source coupled with melt mixing and assimilation have been proposed in order to explain observed petrologic and chemical characteristics of eucrites. EET 90020 is an unbrecciated eucrite that has experienced significant thermal metamorphism, with temperatures of metamorphic equilibration calculated to be ~840-1040°C. Its petrologic history remains contentious, in part due to differences in trace element analyses [10,17, this work], which has led to multiple metamorphic interpretations [8,10-11]. Here, we combined petrologic observations, chemical analyses, and thermodynamic modeling, to interpret micro-domain textures identified in EET 90020 and better constrain its petrologic history. Ultimately, the development of such textures is a direct result of the geologic processes operating on a young Vesta or similar asteroid. Sample description: We identified three textural domains in EET 90020 (Figure 1); (I) A coarse grain domain with granoblastic plagioclase and pyroxene, (II) a medium grain domain with curved grain boundaries between plagioclase and pyroxene, and (III) a fine grain domain dominated by tridymite that fills in interstitial space between spherical plagioclase. Major element chemistry in phases is consistent across domains. Pyroxene have distinctive high Ca lamellae (Wo40.92En28.1Fs31.0) forming from the low-Ca pigeonite host (Wo3.5En33.7Fs62.8). There are small amounts of fayalitic olivine along pyroxene/oxide grain boundaries, where pyroxenes have reacted with ilmenite/chromite clasts. Plagioclase is anorthitic (Avg ~An88), with little variation (An86-92.5). Trace element bulk rock analyses were collected via ICP-MS and individual mineral analyses with LA-ICP-MS (Figure 2). The bulk sample has an observable enrichment in light rare earth elements, with a notable depletion in Eu. Plagioclase is enriched in LREEs, depleted in HREEs, and has a positive Eu anomaly while pyroxene is enriched in HREEs with a negative Eu anomaly. Variations in trace element analyses is likely influenced by the presence of phosphates because are highly enriched in REEs and have a dramatic effect on the bulk domain compositions. Thermodynamic modeling: The software package, Perple_X, was used to calculate mineral phase equilibria over a range of conditions using a Gibbs free energy minimization approach [12]. Models used all major/minor elements except P2O5. Thermodynamic properties from [13] were used to constrain endmember phase stabilities. Activity models were used to describe mixing in phases with solid solution. Isochemical P-T phase diagrams were constructed for the bulk thin section, and the coarse, medium and fine grain domain compositions. Domain compositions were determined using microprobe analyses of phases identified in each domain and observed modal mineral abundancies. Thermodynamically stable pyroxene compositions were extracted from model results and compared to pyroxene compositions collected via EMPA, allowing us to calculate temperatures for metamorphic equilibrium. Results: Results that use the coarse domain composition (Fig. 3a) demonstrate overlap at T ~ 1020°C indicating high T equilibration. There was no overlap for the medium and fine grain domains, or the bulk composition (e.g., Fig. 3b) indicating that these are not equilibrium assemblages. These results were replicated using data from [8,20]. Discussion: The disequilibrium results from the bulk rock, fine grain and medium grain models imply that EET 90020 was modified during and/or after peak metamorphism (open system behavior). However, this is in contrast to the coarse domain where it appears as if equilibrium was maintained. We suggest that this conflict is explained by highly localized equilibrium occurring at millimeter length-scales, which has been observed in terrestrial metamorphism where aqueous fluid infiltrate [14] or melt loss occurs [15]. It is unlikely that aqueous alteration was significant in modifying the bulk composition of EET 90020, because it lacks hydrated minerals. However, the presence of melt is supported by the presence of an abundance of curved grain boundaries and spherical grains in the medium and fine grain domains This contrasts the coarse domain, where grain boundaries are angular. Given the evidence for disequilibrium in the medium and fine grain domains, it would be inappropriate to draw additional conclusions about textural evolution using thermodynamic models of those domains. However, modeling results of the coarse grain domain, where equilibrium was maintained, can provide useful insights into the geologic evolution of EET 90020. We approximate maximum metamorphic temperatures, using the Ca component in pyroxene, at ~1020°C (Fig. 4), which is consistent with previous two-pyroxene thermometry [11]. At this temperature, up to 10 vol % melt can be produced in the coarse grain domain, which is at the boundary of minimum melt needed in order to segregate and form a melt network [16]. Tridymite and plagioclase would be the first minerals to melt out during heating starting ~990°C. This is consistent with the observed melt textures formed by tridymite and plagioclase in the fine grain domain. We suggest that a partial melting model best explains the textural development of EET 90020. Upon heating, melt generated was either trapped, resulting in no net change in the localized rock composition, or migrated, resulting in disequilibrium between pyroxene and the surrounding matrix. A positive Eu anomaly in plagioclase indicates that all of the plagioclase was melted previously. This is consistent with previous studies that have suggested that EET 90020 represents a residual eucrite that experienced partial melting and subsequent melt loss [8]. We speculate that partial melting could have occurred when EET 90020 was heated in the asteroid’s lower crust or adjacent to an intrusion [7]. Future work will study other, texturally heterogeneous samples to see if EET 90020 presents a unique circumstance or whether crustal partial melting was ubiquitous on the eucrite asteroid.

Eucrites↗

Active region magnetic fields inferred from simultaneous VLA microwave maps, X-ray spectroheliograms, and magnetograms

The VLA maps at 6-cm wavelength discussed here are generated from observations of a solar active region (NOAA 2363) on March 29 and 30, 1980. The X-ray spectroheliograms were acquired for this region in the lines of O VIII, Ne IX, Mg XI, Si XIII, S XV, and Fe XXV. It is found that the peaks of X-ray and 6-cm emission do not coincide but that the sources in the two wavelength domains tend to overlap. These facts are seen as evidence for the existence of opacity mechanisms other than thermal bremsstrahlung. To quantify this assertion, differential emission measures are computed to derive densities and temperatures. Using these and calculated force-free magnetic fields from Kitt Peak magnetograms, an assessment is made of the mechanism of gyroresonance absorption at low harmonics of the electron gyrofrequency as the source of opacity responsible for the microwave features. It is concluded that large-scale currents must be present in the active region loops to account for the bright 6-cm sources far from sunspots.

Schmahl, E. J.↗

Experiments with elliptic problem solvers on the Cedar multicluster

The implementation and performance of algorithms for the solution of elliptic problems on the Cedar multiprocessor is examined. The algorithms considered are conjugate gradient schemes with or without preconditioning on a rectangular domain and domain decomposition techniques with overlapping (Schwarz Alternating Method) and nonoverlapping subdomains on a T-shaped domain. Some preliminary results from a current research effort are presented.

Frank, G.↗

Ar-Ar Age of Shergottite Dhofar 378: Formation or Early Shock Event?

The Ar-39-Ar40 data for 16 stepwise temperature extractions of mixed mesostasis plus plagioclase show the following major characteristics. Changes in the K/Ca ratio and in the differential rate of Ar-39 release with extraction temperature suggest three distinct, but overlapping Ar diffusion domains: <13%, 13-45%, and >45% cumulative Ar-39 release:. The youngest Ar-Ar age, approx.162-165 Myr is observed at approx.28-40% Ar-39 release, which we attribute primarily to the mesostasis. Extractions releasing >45% Ar-39, probably from plagioclase, suggest older Ar-Ar ages and indicate release of trapped martian Ar-40. An isochron plot for 8 extractions, releasing 3-45% of the Ar-39 and corrected for 36Arcos using directly measured 36Arcos, gives an Ar-Ar age of 143+/-4 Myr (where the +/- ignores the uncertainty in applying a correction for Ar-36cos). Applying a correction assuming only one-half of the measured Ar-36cos gives an age of 159+/-2 Myr. Correcting for cos-Ar-36 using the minimum measured Ar-36/Ar-37 ratio gives a minimum possible age of 138+/-5 Myr. All of these ages are within combined uncertainties of the Sm-Nd age of 157+/-24 Myr [4]. The trapped Ar-40/Ar-36 ratio obtained from the isochron is largely defined by the highest [K] data.

Park, J.↗

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Nielsen, Tanner B.↗