High order marching schemes for the wave equation in complex geometry
Journal of Computational Physics
Journal of Computational and Applied Mathematics
High order finite difference methods for wave propagation in discontinuous media
Journal of Computational Physics
Numerical stability for finite difference approximations of Einstein's equations
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
Journal of Computational and Applied Mathematics
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
Journal of Computational Physics
Maximum norm error estimates of efficient difference schemes for second-order wave equations
Journal of Computational and Applied Mathematics
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
Journal of Scientific Computing
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
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Difference approximations are derived for the second order wave equation in one and two space dimensions, without first writing it as a first order system. Both the Dirichlet and the Neumann problems are treated for the one-dimensional case. Relations between the boundary error and the interior phase error are derived for a fully second order accurate discretization as well as a scheme that is fourth order accurate in the interior and second order accurate at the boundary. General two-dimensional domains are considered for the Dirichlet problem where the domain is embedded in a Cartesian grid and the boundary conditions are approximated by interpolation. A stable conservative scheme is derived where the time step is determined only by the interior discretization formula. Discretization cells cut by the boundary are treated implicitly, but the resulting scheme becomes explicit because the implicit dependence only is pointwise. Numerical examples are provided to verify the stability and accuracy of the proposed method.