Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
Journal of Computational Physics
Short Note: A stability analysis for the spectral volume method on tetrahedral grids
Journal of Computational Physics
Spectral difference method for compressible flow on unstructured grids with mixed elements
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
Journal of Computational Physics
An implicit high-order spectral difference approach for large eddy simulation
Journal of Computational Physics
LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.50 |
In this paper, the spectral volume method is extended to the two-dimensional Euler equations with curved boundaries. It is well-known that high-order methods can achieve higher accuracy on coarser meshes than low-order methods. In order to realize the advantage of the high-order spectral volume method over the low order finite volume method, it is critical that solid wall boundaries be represented with high-order polynomials compatible with the order of the interpolation for the state variables. Otherwise, numerical errors generated by the low-order boundary representation may overwhelm any potential accuracy gains offered by high-order methods. Therefore, more general types of spectral volumes (or elements) with curved edges are used near solid walls to approximate the boundaries with high fidelity. The importance of this high-order boundary representation is demonstrated with several well-know inviscid flow test cases, and through comparisons with a second-order finite volume method.