Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
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
Journal of Computational Physics
Journal of Computational Physics
Extension of the spectral volume method to high-order boundary representation
Journal of Computational Physics
High-order accurate implementation of solid wall boundary conditions in curved geometries
Journal of Computational Physics
Journal of Computational Physics
Partitions for Spectral (Finite) Volume Reconstruction in the Tetrahedron
Journal of Scientific Computing
Short Note: A stability analysis for the spectral volume method on tetrahedral grids
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.46 |
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.