Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Implicit weighted ENO schemes for the three-dimensional incompressible Navier-Stokes equations
Journal of Computational Physics
Composite Schemes for Conservation Laws
SIAM Journal on Numerical Analysis
Real gas computation using an energy relaxation method and high-order WENO schemes
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
On Nonconservative Algorithms for Grid Interfaces
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Multi-domain hybrid spectral-WENO methods for hyperbolic conservation laws
Journal of Computational Physics
Development of nonlinear weighted compact schemes with increasingly higher order accuracy
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Improvement of Convergence to Steady State Solutions of Euler Equations with the WENO Schemes
Journal of Scientific Computing
High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
SIAM Journal on Scientific Computing
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High order finite difference WENO methods have the advantage of simpler coding and smaller computational cost for multi-dimensional problems, compared with finite volume WENO methods of the same order of accuracy. However a main restriction is that conservative finite difference methods of third and higher order of accuracy can only be used on uniform rectangular or smooth curvilinear meshes. In order to overcome this difficulty, in this paper we develop a multidomain high order WENO finite difference method which uses an interpolation procedure at the subdomain interfaces. A simple Lagrange interpolation procedure is implemented and compared to a WENO interpolation procedure. Extensive numerical examples are shown to indicate the effectiveness of each procedure, including the measurement of conservation errors, orders of accuracy, essentially non-oscillatory properties at the domain interfaces, and robustness for problems containing strong shocks and complex geometry. Our numerical experiments have shown that the simple and efficient Lagrange interpolation suffices for the subdomain interface treatment in the multidomain WENO finite difference method, to retain essential conservation, full high order of accuracy, essentially non-oscillatory properties at the domain interfaces even for strong shocks, and robustness for problems containing strong shocks and complex geometry. The method developed in this paper can be used to solve problems in relatively complex geometry at a much smaller CPU cost than the finite volume version of the same method for the same accuracy. The method can also be used for high order finite difference ENO schemes and an example is given to demonstrate a similar result as that for the WENO schemes.