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
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Journal of Computational Physics
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
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
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
A first-order system approach for diffusion equation. I: Second-order residual-distribution schemes
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
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 Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
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
Journal of Computational Physics
LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method
Journal of Scientific Computing
WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
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In this paper, the spectral volume (SV) method is extended to solve viscous flow governed by the Navier-Stokes equations. Several techniques to discretize the viscous fluxes have been tested, and a formulation similar to the local discontinuous Galerkin (DG) approach developed for the DG method has been selected in the present study. The SV method combines two key ideas, which are the bases of the finite volume and the finite element methods, i.e., the physics of wave propagation accounted for by the use of a Riemann solver and high-order accuracy achieved through high-order polynomial reconstructions within spectral volumes. The formulation of the SV method for a 2D advection-diffusion equation and the compressible Navier-Stokes equations is described. Accuracy studies are performed using problems with analytical solutions. The solver is used to compute laminar viscous flow problems to shown its potential.