The Journal of the Acoustical Society of America · 1994 · 142 citations · 0 references
ComputingHigh-performance ComputingPhysicsAcousticsComputational AcousticsComputational PhysicsAcoustic ModelingAcoustic SimulationFinite Difference MethodsGrid GenerationMesh GenerationNumerical AcousticsAccuracyCartesian GridsFinite Difference SimulationFinite Difference Time Domain ModelingFinite Difference Time Domain SimulationMesh Generation For AcousticsTime-domain Acoustic SimulationTime-domain Acoustics
FDTD is a time‑domain numerical method for acoustical fields, but its reliance on an analytical grid limits flexibility. The study derives FDTD equations enabling nonuniform grids to improve accuracy. The authors derive equations for nonuniform grids, leaving automatic mesh generation unaddressed. Simulations show that quasi‑Cartesian grids better capture tilted and curved boundaries, yielding higher accuracy per CPU resource compared to Cartesian grids.
The finite-difference time-domain (FDTD) approximation can be used to solve acoustical field problems numerically. Mainly because it is a time-domain method, it has some specific advantages. The basic formulation of the FDTD method uses an analytical grid for the discretization of an unknown field. This is a major disadvantage. In this paper, FDTD equations that allow us to use a nonuniform grid are derived. With this grid, tilted and curved boundaries can be described more easily. This gives a better accuracy to CPU–resource ratio in a number of circumstances. The paper focuses on the new formulation and its accuracy. The problem of automatically generating the mesh in a general situation is not addressed. Simulations using quasi-Cartesian grids are compared to Cartesian grid results.