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
Journal of Computational Physics
Multidomain spectral solution of the Euler Gas-dynamics equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
Journal of Computational Physics
Non-oscillatory spectral element Chebyshev method for shock wave calculations
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
Exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids
Journal of Computational Physics
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)
Journal of Computational Physics
Mass flux schemes and connection to shock instability
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
Extension of the spectral volume method to high-order boundary representation
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
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
A spectral finite volume transport scheme on the cubed-sphere
Applied Numerical Mathematics
Short Note: On the connection between the spectral volume and the spectral difference method
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
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
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
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 31.53 |
The framework for constructing a high-order, conservative spectral (finite) volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high-order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner..The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and nonlinear model problems with and without discontinuities.