Simulation techniques

摘要

A method for assessing wave propagation arising in a physical system by obtaining a numerical approximation of the physical system to be simulated, the method comprising
defining a computational domain comprising a first grid having a plurality of first-grid cells and a first-grid time step, a second grid being a refinement of the first grid and having a plurality of second-grid cells and a second-grid time step, and an intermediate grid having a plurality of intermediate-grid cells of equal size to the first-grid cells and having the second-grid time step, wherein each cell has one or more solution points at which values representing a physical quantity of the physical system to be simulated may be obtained;
performing a first update procedure to obtain values representing the physical quantity after a said first-grid time step, the values being obtained for at least one solution point of at least one first-grid cell;
performing a coupling procedure using values from the first grid to obtain values at a perimeter of the second grid; and
performing a second update procedure, using the values at the perimeter of the second grid, to obtain values representing the physical quantity after a said second-grid time step, the values being obtained for at least one solution point of at least one second-grid cell;
wherein the coupling procedure comprises
performing temporal coupling by using values from the first grid to obtain values at a perimeter of the intermediate grid;
performing an intermediate update procedure to obtain values representing the physical quantity after the said second-grid time step of the second update procedure, the values being obtained for at least one solution point of at least one intermediate-grid cell; and
performing spatial coupling by using values from the intermediate grid to obtain the values at the perimeter of the second grid used in the second update procedure;
wherein defining the computational domain comprises defining the perimeter of the intermediate grid to be wider than the perimeter of the second grid on at least one side of the second grid by a distance equal to at least two times the size of one of the first-grid cells in that dimension.