Robust low‐dissipative scheme for curvilinear grids

This work describes a detailed mathematical procedure in relation to a novel third-order WENO scheme for the inviscid term of a system of nonlinear equations in the generalized grid system. The scheme developed minimizes the linear and nonlinear sources of dissipation error associated with the classical fifth-order WENO scheme. The former is minimized by optimizing the resolving efficiency of the scheme whereas the latter is minimized by fixing the accuracy at the second-order critical point via redefining the nonlinear weights. Moreover, the spectral property of second-order viscous derivative, approximated by the single and double applications of the standard fourth-order central finite difference scheme, is presented. The two-dimensional Euler and Navier-Stokes equations in the generalized grids are mainly pursued. For the robustness in terms of capturing discontinuous and smooth structures, particularly two problems, which are difficult to handle in Cartesian grids, are chosen for discussion. The first one deals with a supersonic shock hitting the circular cylinder and generating all the possible flow inconsistencies. The other one deals with a subsonic flow over a circular cylinder at the incompressible limit. The numerical results are found to be in good agreement with the experimental data.