Examination of Sub-Grid Technique for Simulation of Sound Wave Propagation Using Constrained Interpolation Profile Method with Method of Characteristics

Abstract

The constrained interpolation profile (CIP) method is a novel low-dispersive numerical scheme. It is a kind of method of characteristics (MOC). In our past study, we applied the CIP method to numerical analyses of sound wave propagation. For simulations of complicated heterogeneous media or large-scale simulations of wave propagation, a new grid system is indispensable. In this study, we examined a sub-grid technique for the CIP acoustic wave simulation. It is clarified that this technique has the advantages of its small memory requirements and less calculation time.

Evaluation of numerical simulation of acoustic wave propagation using method of characteristics-based constrained interpolation profile (CIP-MOC) method with non-uniform grids

“…The type-M CIP method is a simple technique with smaller memory use and less calculation time required than the type-C CIP method. Figure 1 shows a schematic of the non-uniform grid and sub-grid system [15]. The memory required for the nonuniform grid system is slightly larger than that for the sub-grid shown in the figure.…”

“…In previous studies, subgrid techniques [14,15] were proposed for the CIP method to overcome these problems. However, handling the derivatives in the perpendicular directions at the interface between grids of different sizes is complicated in these techniques.…”

Performance Comparison of Subgrid Techniques in Acoustic Simulation Using the Type-M and Type-C Constrained Interpolation Profile Methods

“…10) This technique for the type-C CIP method has been partially introduced. 11) As for the type-M CIP method, 4,8) however, it has not been investigated. The type-M CIP method is a simple technique with smaller memory use and less calculation time required than the type-C CIP method.…”

“…In the first step, p and @ y p are interpolated in the AEy-direction by third-order Hermite interpolation, whereas v x , @ x p, and @ x v x are interpolated by first-order Lagrange interpolation. Although the procedures of the subgrid techniques for the type-M and type-C CIP methods are basically similar, 11) the type-M CIP method employs the Lagrange interpolation. 12) Next, we calculate advection equations in the AEx-direction in the second step.…”

“…We also show the numerical results obtained using the subgrid technique for type-C CIP analysis. 11) Calculation parameters of both analyses are on equal terms. It is confirmed that the boundary in the subgrids has good permeability characteristics with low reflection.…”