The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for ellipti...The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.展开更多
In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for t...In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for treating material interfaces for Maxwell’s equations.In addition to the idea of the UEBM to evolve solutions at interfaces,we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces.As a result,Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method,in contrast to the original second-order UEBM based on a Lax-Wendroff type difference.The final scheme allows time step sizes independent of the interface locations.Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method.We tested the scheme for several wave problems with various material interface locations,including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis.展开更多
基金supported by the U.S.Department of Energy under Contract No.DE-AC02-98CH10886 and by the State of New York
文摘The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.
文摘In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for treating material interfaces for Maxwell’s equations.In addition to the idea of the UEBM to evolve solutions at interfaces,we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces.As a result,Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method,in contrast to the original second-order UEBM based on a Lax-Wendroff type difference.The final scheme allows time step sizes independent of the interface locations.Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method.We tested the scheme for several wave problems with various material interface locations,including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis.
