Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
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
Efficient Algebraic Multigrid Algorithms and Their Convergence
SIAM Journal on Scientific Computing
A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
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
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An adaptive finite volume method for 2D steady Euler equations with WENO reconstruction
Journal of Computational Physics
Hi-index | 31.46 |
A robust high-order algorithm is proposed to solve steady Euler equations on unstructured grids. The main ingredients of the algorithm include a standard Newton method as the outer iterative scheme and a linear multigrid method as the inner iterative scheme with the block lower-upper symmetric Gauss-Seidel (LU-SGS) iteration as its smoother. The Jacobian matrix of the Newton-iteration is regularized by the local residual, instead of using the commonly adopted time-stepping relaxation technique based on the local CFL number. The local Jacobian matrix of the numerical fluxes are computed using the numerical differentiation, which can significantly simplify the implementations by comparing with the manually derived approximate derivatives. The approximate polynomial of solution on each cell is reconstructed by using the values on centroid of the cell, and limited by the WENO hierarchical limiting strategy proposed by Xu et al. [Z.L. Xu, Y.J. Liu, C.W. Shu, Hierarchical reconstruction for discontinuous galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells, Journal of Computational Physics 228 (2009) 2194-2212]. It is found that the proposed algorithm is insensitive to the parameters used. More precisely, in our computations, only one set of the parameters (namely, the proportional constant @a for the local residual, the relaxation parameter @t in the Newton-iteration, the weight @m in the WENO scheme and the number of smoothing steps in the multigrid solver) is employed for various geometrical configurations and free-stream configurations. The high-order and robustness of our algorithm are illustrated by considering two-dimensional airfoil problems with different geometrical configurations and different free-stream configurations.