GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
On the effect of numerical errors in large eddy simulations of turbulent flows
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
Conservative high-order finite-difference schemes for low-Mach number flows
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A semi-implicit method for resolution of acoustic waves in low Mach number flows
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
A robust high-order compact method for large eddy simulation
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
Higher entropy conservation and numerical stability of compressible turbulence simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows
Journal of Computational Physics
Generalized conservative approximations of split convective derivative operators
Journal of Computational Physics
Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates
Journal of Computational Physics
On the spectral and conservation properties of nonlinear discretization operators
Journal of Computational Physics
Journal of Computational Physics
A 3D Unsplit Forward/Backward Volume-of-Fluid Approach and Coupling to the Level Set Method
Journal of Computational Physics
Journal of Computational Physics
On a robust ALE method with discrete primary and secondary conservation
Journal of Computational Physics
Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
Hi-index | 31.49 |
The form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Morinishi et al. [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 124 (1998) 90], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow. These forms are analytically equivalent if the continuity is satisfied, and the skew-symmetric form is secondary conservative without the aid of the continuity, while the divergence form is primary conservative. The relations between the present and existing quasi-skew-symmetric forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-symmetric form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow.