A Third-Order Weighted Essentially Non-Oscillatory Compact Least-Squares Scheme for Hyperbolic Conservation Laws on Non-Uniform Grids

A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with optimal linear weights for broad-spectrum accuracy and non-linear weights for essentially non-oscillatory property. Through explicit second-order polynomials given for each control volume, the scheme maintains high accuracy on structured meshes with non-uniform grids. By integrating an improved shock detector developed in this work, coefficients with adaptive levels of dissipation are applied to achieve both the high resolution in smooth regions and high robustness in discontinuous regions. Furthermore, the proposed scheme is extended to the Euler equations through a characteristic decomposition technique. Numerical examples including both linear convection equation and nonlinear Euler/Navier-Stokes equations demonstrate the robustness and high-resolution of the proposed method.