GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Spectral element multigrid. I. Formulation and numerical results
Journal of Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes
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
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An efficient implicit discontinuous spectral Galerkin method
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
Journal of Computational Physics
On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations
Journal of Scientific Computing
Partitions of a Simplex Leading to Accurate Spectral (Finite) Volume Reconstruction
SIAM Journal on Scientific Computing
Journal of Computational Physics
Extension of the spectral volume method to high-order boundary representation
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Partitions for Spectral (Finite) Volume Reconstruction in the Tetrahedron
Journal of Scientific Computing
Journal of Computational Physics
LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method
Journal of Scientific Computing
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
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
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In this paper, we improve the Navier---Stokes flow solver developed by Sun et al. based on the spectral volume method (SV) in the following two aspects: the development of a more efficient implicit/p-multigrid solution approach, and the use of a new viscous flux formula. An implicit preconditioned LU-SGS p-multigrid method developed for the spectral difference (SD) Euler solver by Liang is adopted here. In the original SV solver, the viscous flux was computed with a local discontinuous Galerkin (LDG) type approach. In this study, an interior penalty approach is developed and tested for both the Laplace and Navier---Stokes equations. In addition, the second method of Bassi and Rebay (also known as BR2 approach) is also implemented in the SV context, and also tested. Their convergence properties are studied with the implicit BLU-SGS approach. Fourier analysis revealed some interesting advantages for the penalty method over the LDG method. A convergence speedup of up to 2-3 orders is obtained with the implicit method. The convergence was further enhanced by employing a p-multigrid algorithm. Numerical simulations were performed using all the three viscous flux formulations and were compared with existing high order simulations (or in some cases, analytical solutions). The penalty and the BR2 approaches displayed higher accuracy than the LDG approach. In general, the numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.