To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains, inverse Lax-Wendroff (ILW) procedures were developed as a very effective approach in the literature. See more A spatial discretization of (1) by a high-order WENO scheme leads to a large nonlinear system of algebraic equations with the size … See more In this section, we outline the ILW numerical boundary treatment in both one-dimensional (1D) and two-dimensional (2D) problems. The ILW methods have been developed and studied extensively in, e.g., [21, 22], so … See more The similar fast sweeping techniques can also be applied to a TVD-RK scheme as that in [24]. However, it was found in [24] that the scheme resulted by applying these fast sweeping techniques to the TVD-RK type … See more WebWe develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes. The method is an extension of the inverse...

A high order moving boundary treatment for convection-diffusion ...

WebAug 2, 2024 · The main challenge is how to obtain the solutions at ghost points resulting from the wide stencil of the interior high order scheme. We address this problem by combining the idea of using the RK schemes at the boundary and an inverse Lax-Wendroff procedure. The former preserves the accuracy of the RK schemes and the … WebJul 10, 2024 · In particular, the inverse Lax–Wendroff (ILW) procedure uses the given boundary condition and the partial differential equations to apply the boundary … sunny hills florida lots for sale

A Fixed-Point Fast Sweeping WENO Method with Inverse …

WebNov 23, 2015 · The high order inverse Lax-Wendroff (ILW) procedure is extended to boundary treatment involving complex geometries on a Cartesian mesh. Our method ensures that the numerical resolution at the vicinity of the boundary and the inner domain keeps the fifth order accuracy for the system of the reactive Euler equations with the two … WebMar 20, 2012 · For the sake of accuracy and stability, a so-called inverse Lax–Wendroff (ILW) procedure was developed. This procedure was first proposed by Goldberg and Tadmor [6], [7] for analyzing numerical boundary conditions of linear hyperbolic equations in one dimension with boundaries aligned with grid lines. Web, An inverse Lax–Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary, J. Comput. Phys. 426 (2024). Google Scholar [9] Li T., Shu … sunny hills florida real estate