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
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
The Mathematica book (4th edition)
The Mathematica book (4th edition)
Stable Spectral Methods on Tetrahedral Elements
SIAM Journal on Scientific Computing
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
On the Stability and Accuracy of the Spectral Difference Method
Journal of Scientific Computing
Short Note: A stability analysis for the spectral volume method on tetrahedral grids
Journal of Computational Physics
Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Hierarchical reconstruction for spectral volume method on unstructured grids
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
Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case
Journal of Computational Physics
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
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Journal of Computational Physics
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
Journal of Computational Physics
The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Hi-index | 31.56 |
In this paper, the fourth in a series, the spectral volume (SV) method is extended to multi-dimensional systems -- the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems, and to verify that high order solution accuracy up to fourth-order can be achieved for the systems of conservation laws. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. An accuracy study is performed first to numerically verify that the designed order of accuracy can be obtained for smooth flow solutions. Then, solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.