Finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains

A finite difference time-dependent numerical method for the wave equation, supported by recently derived novel elliptic grids, is analyzed. The method is successfully applied to single and multiple two-dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries. The new grids have nearly uniform cell area (J-grids) and nearly uniform grid line spacing (αγ-grids). Numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state. The restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing. As a consequence, moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost. Also, numerical solutions for wave problems inside annular regions of complex shapes are obtained. The use of the new grids results in late time stability in contrast with other classical finite difference time-dependent methods.