A method for assessing wave propagation in a physical system by numerical simulation; a computational domain comprises first grid cells with a first-grid time step, refined second grid cells with a second-grid time step, and intermediate grid cells of first-grid cell size and second-grid time step, with solution points located on the cells; obtaining values of a physical quantity after a first-grid time step at a solution point of one first-grid cell; using values from the first grid to obtain values at a perimeter of the intermediate grid; obtaining values of the physical quantity after the second-grid time step; using values from the intermediate grid to obtain the values at the perimeter of the second grid; using the values at the perimeter of the second grid, to obtain values of the physical quantity after a second-grind time step for solution points of the second-grind cell.