scholarly journals Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

2013 ◽  
Vol 35 (5) ◽  
pp. A2163-A2187 ◽  
Author(s):  
Sandra May ◽  
Marsha Berger
Keyword(s):  
Finite Volume ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Slope Limiters

scholarly journals A Stability Analysis of Finite-Volume Advection Schemes Permitting Long Time Steps

2007 ◽  
Vol 135 (7) ◽  
pp. 2658-2673 ◽  
Author(s):  
Peter Hjort Lauritzen
Keyword(s):  
Stability Analysis ◽  
Finite Volume ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Courant Number ◽  
Von Neumann ◽  
Dispersion Properties ◽  
Advection Schemes ◽  
Long Time ◽  
The Stability

Abstract Finite-volume schemes developed in the meteorological community that permit long time steps are considered. These include Eulerian flux-form schemes as well as fully two-dimensional and cascade cell-integrated semi-Lagrangian (CISL) schemes. A one- and two-dimensional Von Neumann stability analysis of these finite-volume advection schemes is given. Contrary to previous analysis, no simplifications in terms of reducing the formal order of the schemes, which makes the analysis mathematically less complex, have been applied. An interscheme comparison of both dissipation and dispersion properties is given. The main finding is that the dissipation and dispersion properties of Eulerian flux-form schemes are sensitive to the choice of inner and outer operators applied in the scheme that can lead to increased numerical damping for large Courant numbers. This spurious dependence on the integer value of the Courant number disappears if the inner and outer operators are identical, in which case, under the assumptions used in the stability analysis, the Eulerian flux-form scheme becomes identical to the cascade scheme. To explain these properties a conceptual interpretation of the flux-based Eulerian schemes is provided. Of the two CISL schemes, the cascade scheme has superior stability properties.

scholarly journals Upwind Finite Volume Schemes for One and Two Dimensional Euler Equations

2003 ◽  
Author(s):  
Thierry Gallouet ◽  
Jean-Marc Hérard ◽  
Raphaele Herbin ◽  
Nicolas Jullian ◽  
Nicolas Seguin
Keyword(s):  
Euler Equations ◽  
Finite Volume ◽  
Two Dimensional ◽  
Finite Volume Schemes

scholarly journals Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

2013 ◽  
Vol 14 (5) ◽  
pp. 1174-1206 ◽  
Author(s):  
Walter Boscheri ◽  
Michael Dumbser
Keyword(s):  
Finite Volume ◽  
Space Time ◽  
High Order ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Triangular Meshes ◽  
Finite Volume Schemes ◽  
Local Space ◽  
One Step ◽  
Time Basis

AbstractIn this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in. For that purpose, a new element-local weak formulation of the governing PDE is adopted on moving space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes withstraightedges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.

Sign in / Sign up

Export Citation Format

Share Document