Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid

Abstract

Wave propagation in an isotropic acoustic medium occupied by a moving fluid is governed by an anisotropic eikonal equation. Since this anisotropic eikonal equation is associated with an inhomogeneous Hamiltonian, most of existing anisotropic eikonal solvers are either inapplicable or of unpredictable behavior in convergence. Realizing that this anisotropic eikonal equation is defined by a sum of two well-understood first-order differential operators, we propose novel operator-splitting based fast sweeping methods to solve this generalized eikonal equation. We develop various operator-splitting methods relying on the Peaceman--Rachford scheme, the Douglas--Rachford scheme, the $\theta$-scheme, and the regularized $\theta$-scheme. After applying the operator-splitting strategy, each splitting step corresponds to a much simpler Hamilton--Jacobi equation so that we can apply the Lax--Friedrichs sweeping method to solve these splitted equations efficiently and easily. Two- and three-dimensional examples demons...