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Results for “Semi-Lagrangian”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Bates, J. R.↗
NASA NTRS1993

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Li, Y.↗
DOE OSTI2024

An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Semi-Lagrangian integration of a grid-point shallow water model on the sphere

This paper describes a semi-Lagrangian technique for integrating the equations of motion on the global domain. The technique uses an auxiliary spherical coordinate system at each near-polar gridpoint of the latitude-longitude grid; the auxiliary system is obtained by a rotation such that the new equator passes through the gridpoint in question and the new coordinate directions coincide with those of the original system at that point. The technique was applied to the shallow water equations, incorporating a semiimplicit treatment of the adjustment terms on a C-grid, with two-time levels. A five day integration was successfully carried out for a situation involving strong cross-polar flow. No filtering or diffusion was required to maintain stability over a five day period.

Mcdonald, A.↗
NASA NTRS1989

Semi-Lagrangian integration of a gridpoint shallow water model on the sphere

A stable, semi-Lagrangian, semi-implicit, two-time-level, gridpoint integration scheme for the shallow water equations on the sphere is presented. A rotated spherical coordinate system is used to integrate the equations of motion at each gridpoint poleward of a certain latitude, thus overcoming problems associated with the polar singularity. The results of medium term integrations of large scale test patterns using a long time step are presented.

Mcdonald, A.↗
NASA NTRS1993

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Bates, J. R.↗
NASA NTRS1993

A semi-Lagrangian approach to the shallow water equation

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

Bates, J. R.↗
NASA NTRS1994

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Max J. Suarez↗
NASA NTRS1994

The permeability of the Antarctic vortex edge

Mixing and cross-vortex mass transport along isentropic surfaces in the lower stratosphere are investigated with a 'contour advection' technique and a semi-Lagrangian transport model for the Antarctic winter of 1993 using analyzed winds from the United Kingdom Meteorological Office data assimilation system. Results from the 'contour advection' technique show that at the vortex edge there exists a potential vorticity (PV) contour that has the smallest lengthening rate. This PV contour is referred to as the 'line of separation' because it essentially separates the inner and outer vortex. The average e-folding time for the lengthening of the 'line of separation' increases monotonically with altitude, ranging from about 7 days on the 350 K isentropic surface to about 105 days on the 500 K isentropic surface. The results also suggest the existence of a transition layer around the 400 K isentropic surface, above which the vortex is nearly completely isolated from the midlatitudes and below which the vortex is less isolated. Results from a semi-Lagrangian transport model with an idealized tracer initially inside the inner vortex show that at 425 K and above virtually no tracer is transported out of the vortex during a 40-day integration starting from July 21, 1993. At 400 K and below a small amount of the tracer is transported out of the vortex while the bulk of the tracer remains confined within the inner vortex.

Chen, Ping↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2026

Quantum kinetic modeling of KEEN waves in a warm-dense regime

We report the first fully kinetic, quantum study of kinetic electrostatic electron nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrows harmonic locking to the fundamental, and hastens post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner–Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. We focus on collisionless dynamics in a weakly coupled regime, providing a controlled baseline before collisional extensions. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of non-equilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗
NASA NTRS1991

Simulation of the Pinatubo aerosol cloud in general circulation model

The global transport and dispersion of the Pinatubo aerosol cloud are simulated by means of a high-resolution stratospheric version of the NCAR Community Climate Model (CCM2) with an annual cycle. A passive tracer was injected into the model stratosphere over the Philippine Islands on June 15, and the transport was simulated for 180 d using an accurate semi-Lagrangian advection scheme. The simulated volcanic aerosol cloud initially drifted westward and expanded in longitude and latitude. The bulk of the aerosol cloud dispersed zonally to form a continuous belt in longitude, and remained confined to the tropics, centered near the 20-mb level for the entire 180-d model run, although a small amount was transported episodically into the upper troposphere in association with convective disturbances. Aerosol transported to the troposphere was dispersed within a few weeks into the Northern Hemisphere extratropics. In the Southern Hemisphere, the aerosol was mixed into the region equatorward of the core of the polar night jet during the first 50 d, but penetration into southern polar latitudes was delayed until the final warming in November.

Boville, Byron A.↗
NASA NTRS1994

Simulation of the modern arctic climate by the NCAR CCM1

The National Center of Atmospheric Research (NCAR) Community Climate Model Version 1 (CCM1's) simulation of the modern arctic climate is evaluated by comparing a five-year seasonal cycle simulation with the European Center for Medium-Range Weather Forecasts (ECMWF) global analyses. The sea level pressure (SLP), storm tracks, vertical cross section of height, 500-hPa height, total energy budget, and moisture budget are analyzed to investigate the biases in the simulated arctic climate. The results show that the model simulates anomalously low SLP, too much storm activity, and anomalously strong baroclinicity to the west of Greenland and vice versa to the east of Greenland. This bias is mainly attributed to the model's topographic representation of Greenland. First, the broadened Greenland topography in the model distorts the path of cyclone waves over the North Atlantic Ocean. Second, the model oversimulates the ridge over Greenland, which intensifies its blocking effect and steers the cyclone waves clockwise around it and hence produces an artificial circum-Greenland trough. These biases are significantly alleviated when the horizontal resolution increases to T42. Over the Arctic basin, the model simulates large amounts of low-level (stratus) clouds in winter and almost no stratus in summer, which is opposite to the observations. This bias is mainly due to the location of the simulated SLP features and the negative anomaly of storm activity, which prevent the transport of moisture into this region during summer but favor this transport in winter. The moisture budget analysis shows that the model's net annual precipitation (P-E) between 70 deg N and the North Pole is 6.6 times larger than the observations and the model transports six times more moisture into this region. The bias in the advection term is attributed to the positive moisture fixer scheme and the distorted flow pattern. However, the excessive moisture transport into the Arctic basin does not solely result from the advection term. The contribution by the moisture fixer is as large as from advection. By contrast, the semi-Lagrangian transport scheme used in the CCM2 significantly improves the moisture simulation for this region; however, globally the error is as serious as for the positive moisture fixer scheme. Finally, because the model has such serious problems in simulating the present arctic climate, its simulations of past and future climate change for this region are questionable.

Bromwich, David H.↗
NASA NTRS1994

Isentropic mass exchange between the Tropics and extratropics in the stratosphere

The isentropic mass exchange between the Tropics and extratropics in the stratosphere is investigated with a semi-Lagrangian transport model for the periods from 1 June to 31 October 1992 and from 1 December 1992 to 30 April 1993 using winds from the U.K. Meteorological Office data assimilation system. Calculations with an idealized, initially zonally symmetric tracer show that in the middle and upper stratosphere the bulk of tropical air is transported into the midlatitudes of the winter hemisphere although there exist quasi-permeable barriers in the subtropics. The transport takes place in the form of planetary-scale 'tongues' of material that are drawn poleward in association with the episodic amplification of planetary-scale waves in high latitudes of the winter hemisphere. Once air of tropical origin is transported to the midlatitudes it is irreversibly mixed with the midlatitude air in the 'surf zone.' Air of tropical origin can, however, hardly penetrate into the interior of the winter polar vortex until the breakdown of the vortex. Transport of tropical air into the midlatitudes of the summer hemisphere is strongly inhibited. In the lower stratosphere, tropical air is transported into the northern and southern midlatitudes. During the period from 1 June to 31 October 1992, the amount of tropical air transported into the Northern Hemisphere is, however, much smaller than that transported into the Southern Hemisphere, and there exist strong gradients in the tracer field in the equatorial region, indicating that there is a quasi-permeable barrier to cross-equator mass exchange. During the period from 1 December 1992 to 30 April 1993, on the other hand, roughly the same amounts of tropical air are transported into the Southern Hemisphere, and there exist strong gradients in the tracer field in the equatorial region, indicating that there is a quasi-permeable barrier to cross-equator mass exchange. During the period from 1 December 1992 to 30 April 1993, on the other hand, roughly the same amounts of tropical air are transported into the northern midlatitudes and into the southern midlatitudes, and there exist no significant transport barriers in the equatorial area.

Chen, Ping↗
NASA NTRS1995

A quasi-permeable barrier in the equatorial lower stratosphere

Analyses of global isentropic maps of potential vorticity from the United Kingdom Meteorological Office (UKMO) data assimilation system reveal that there is a region of strong meridional potential vorticity (PV) gradients in the equatorial lower stratosphere. A semi-Lagrangian tracer transport model is used to show that this region of strong PV gradients acts as a quasipermeable barrier to cross-equator mass exchange on isentropic surfaces.

Chen, Ping↗