This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such ...

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features o...

Incremental stack-copying was used to implement OR-parallel Prolog efficiently in the MUSE system. The idea of incremental stack-copying is to only copy the difference between the WAM data areas of two processors, instead of copying them entirely. In order to further reduce the communication during stack-copying and make its implementation efficient on distributed memory machines, a new techniq...

A gas-kinetic flux splitting method is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of “particle” collisions in the transport process. Consequently, the artificial dissipation in the new scheme is greatly reduced in comparison with the MHD flux vector splitting method. N...

In this study, a numerical solution of nonhydrostatic atmospheric equations is considered. A robust semi-implicit approach with additional time splitting is applied in order to construct computationally efficient and accurate numerical scheme for modeling of large-scale atmospheric dynamics. Description of the designed numerical algorithm is provided and its accuracy and stability are discussed...

In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is ...

We propose a novel second order in time numerical scheme for Cahn-Hilliard-NavierStokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, ...

Two-dimensional Euler equations have been solved on an unstructured grid. An upwind finite volume scheme, based on Roes flux difference splitting method, is used to discretize the equations. Using advancing front method, an initial Delaunay triangulation has been made. The adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...