Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
An analysis of finite-difference and finite-volume formulations of conservation laws
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
A high order accurate difference scheme for complex flow fields
Journal of Computational Physics
Developing high-order weighted compact nonlinear schemes
Journal of Computational Physics
A wave propagation method for three-dimensional hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
Development of nonlinear weighted compact schemes with increasingly higher order accuracy
Journal of Computational Physics
Journal of Computational Physics
Short Note: Effects of difference scheme type in high-order weighted compact nonlinear schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics
Hi-index | 31.48 |
The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators @d"3 have no effects on the SCL, no extra errors can be introduced as @d"3=@d"2. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator @d"1 which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator @d"1 to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.