GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An analysis of finite-difference and finite-volume formulations of conservation laws
Journal of Computational Physics
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Large-eddy simulation of the shock/turbulence interaction
Journal of Computational Physics
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-symmetric form have not been extended to those for moving grids. In this study, the skew-symmetric form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniform flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.