13 research outputs found
An Improved High Order Finite Difference Method for Non-conforming Grid Interfaces for the Wave Equation
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property
An Improved High Order Finite Difference Method for Non-conforming Grid Interfaces for the Wave Equation
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property
An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form
We consider wave propagation in a coupled fluid-solid region, separated by a
static but possibly curved interface. The wave propagation is modeled by the
acoustic wave equation in terms of a velocity potential in the fluid, and the
elastic wave equation for the displacement in the solid. At the fluid solid
interface, we impose suitable interface conditions to couple the two equations.
We use a recently developed, energy based discontinuous Galerkin method to
discretize the governing equations in space. Both energy conserving and upwind
numerical fluxes are derived to impose the interface conditions. The highlights
of the developed scheme include provable energy stability and high order
accuracy. We present numerical experiments to illustrate the accuracy property
and robustness of the developed scheme