Construction of explicit and implicit symmetric tvd schemes and their applications
Journal of Computational Physics
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
ENO schemes with subcell resolution
Journal of Computational Physics
Journal of Computational Physics
Multidomain spectral solution of the Euler Gas-dynamics equations
Journal of Computational Physics
High resolution schemes for steady flow computation
Journal of Computational Physics
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
Journal of Computational Physics
Implicit solvers for unstructured meshes
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
Journal of Computational Physics
On Families of Pointwise Optimal Finite Volume ENO Approximations
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
Mass flux schemes and connection to shock instability
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Journal of Computational Physics
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
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
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
Spectral difference method for compressible flow on unstructured grids with mixed elements
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Error estimation of a quadratic finite volume method on right quadrangular prism grids
Journal of Computational and Applied Mathematics
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
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
An implicit high-order spectral difference approach for large eddy simulation
Journal of Computational Physics
A high-order gas-kinetic Navier-Stokes flow solver
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
Realizable high-order finite-volume schemes for quadrature-based moment methods
Journal of Computational Physics
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
Journal of Computational Physics
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.60 |
A high-order, conservative, yet efficient method named the spectral volume (SV) method is developed for conservation laws on unstructured grids. The concept of a "spectral volume" is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multidomain spectral methods. Each spectral volume is further subdivided into control volumes, and cell-averaged data from these control volumes are used to reconstruct a high-order approximation in the spectral volume. Then Riemann solvers are used to compute the fluxes at spectral volume boundaries. Cell-averaged state variables in the control volumes are updated independently. Furthermore, total variation diminishing and total variation bounded limiters are introduced in the SV method to remove/reduce spurious oscillations near discontinuities. Unlike spectral element and multidomain spectral methods, the SV method can be applied to fully unstructured grids. A very desirable feature of the SV method is that the reconstruction is carried out analytically, and the reconstruction stencil is always nonsingular, in contrast to the memory and CPU-intensive reconstruction in a high-order k-exact finite volume method. Fundamental properties of the SV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.