Perfectly matched layers for Maxwell's equations in second order formulation
Journal of Computational Physics
High order finite difference methods for wave propagation in discontinuous media
Journal of Computational Physics
Journal of Computational Physics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Journal of Scientific Computing
Stable Boundary Treatment for the Wave Equation on Second-Order Form
Journal of Scientific Computing
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
Journal of Computational Physics
Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
Journal of Computational Physics
A fictitious domain method for acoustic wave propagation problems
Mathematical and Computer Modelling: An International Journal
Upwind schemes for the wave equation in second-order form
Journal of Computational Physics
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
An embedded boundary method for soluble surfactants with interface tracking for two-phase flows
Journal of Computational Physics
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Stability theory and numerical experiments are presented for a finite difference method that directly discretizes the Neumann problem for the second order wave equation. Complex geometries are discretized using a Cartesian embedded boundary technique. Both second and third order accurate approximations of the boundary conditions are presented. Away from the boundary, the basic second order method can be corrected to achieve fourth order spatial accuracy. To integrate in time, we present both a second order and a fourth order accurate explicit method. The stability of the method is ensured by adding a small fourth order dissipation operator, locally modified near the boundary to allow its application at all grid points inside the computational domain. Numerical experiments demonstrate the accuracy and long-time stability of the proposed method.