A third-order weighted nonlinear scheme for hyperbolic conservation laws with inverse Lax-Wendroff boundary treatment.

• The inverse Lax-Wendroff boundary treatment method is developed for a third-order weighted nonlinear scheme. • The linear stability of the scheme is proved by both the method of eigenvalue analysis and the Gustafsson-Kreiss-Sundströom (GKS) theory. • The validity of the scheme is demonstrated by numerical examples in terms of accuracy and stability. Cartesian grids are often used in applications due to the simplicity of grid generation and the efficiency of discretization algorithms. However, for problems with curved boundaries, grid points are often away from the boundaries, leading to the issue of imposing boundary conditions. Recently, it was shown that the inverse Lax-Wendroff (ILW) boundary treatment is very useful for addressing this issue. While most of the investigations focus on the WENO schemes for hyperbolic conservation laws, we present in this paper a new third-order weighted nonlinear scheme, which is based on the framework of weighted compact nonlinear schemes. We show that the scheme is applicable directly on Cartesian grids by using the ILW boundary treatment. To demonstrate the linear stability of the scheme, both the method of eigenvalue analysis and the Gustafsson-Kreiss-Sundström (GKS) theory are employed and analyzed in details. Some numerical tests are also performed to show the accuracy and validity of the proposed method. [ABSTRACT FROM AUTHOR]