Approximation of Boundary Condition in Higher Order Grid-Characteristic Schemes

Abstract

In this paper, we consider the problem of constructing a numerical solution to the system of equations of an acoustic medium in a fixed domain with a boundary. Physically, it corresponds to seismic wave propagation in geological media during seismic exploration of hydrocarbon deposits. The system of first-order partial differential equations under consideration is hyperbolic. Its numerical solution is constructed by applying a grid-characteristic method on an extended spatial stencil. This approach yields a higher order approximation scheme at internal points of the computational domain, but requires a careful construction of the numerical solution near the boundaries. In this paper, an approach that preserves the increased approximation order up to the boundary is proposed. Verification numerical simulations were carried out.