Compact Finite Difference Investigation of Pressure Field Governed by a Three Dimensional Wave Equation

Numerical Simulation of three dimensional wave equation is conducted in a cubic domain which contains two parts, part A and part B. Part A of the domain is a I -shaped empty channel, containing air, and part B, containing a solid medium, is the difference between the whole cubic domain and part A. A Dirichlet type boundary condition is specified at the inlet boundary. At all other boundaries of the cubic domain a null Neumann boundary conditions are imposed. As an initial condition a null pressure distribution is specified everywhere in the cubic domain except at the inlet boundary. All spatial derivatives are calculated using a compact finite difference scheme. Computations are advanced in time using a compact third order Runge-Kutta scheme. These computations have to be performed twice in succession for each sub-time step of the Runge-Kutta scheme. The numerical code is successfully tested against an exact solution. This issue is followed by the discussion of a three-dimensional simulation. These results, for pressure, are then integrated over the entire surface of the end plane to introduce the load applied to the plane. Both results indicates that the compact finite difference simulation of the wave equation produce a satisfactory and reliable result.