Abstract
Boundary procedure is an important phenomenon in numerical simulation. To reduce or eliminate the spurious reflections significantly which is occurred in boundary is a challenging and vital approach. The appropriate artificial numerical boundaries can be applied to eliminate the effect of unnecessary spurious reflections in case of the numerical simulations of wave propagation phenomena problems. Typically, to reduce the artificial reflections, the absorbing boundary conditions are necessary. In this paper, we overview and investigate the appropriate typical absorbing boundary conditions and analyzed the boundary effect of two dimensional wave equation numerically. Reflections over the wide-ranging incident angles are complicated to eliminate, but the absorbing boundary conditions that we have applied are computationally cost efficient, easy to apply and able to reduce reflections significantly. For numerical solution, finite difference method is applied to develop numerical scheme using 2D wave equation. Using the developed numerical scheme, we obtain the numerical solution of the governing equation as an initial boundary value problem and realize the qualitative behavior of the solution in infinite space. The finite difference numerical scheme has been investigated by developing MATLAB programming language code. Numerical results have been discussed and analyzed with presenting different qualitative behavior of the numerical scheme. The accuracy and efficiency of the numerical scheme has been illustrated. The stability analysis was discussed and verified stability condition. Using the numerical scheme and absorbing boundary conditions, the boundary effects and absorption of spurious reflection of boundary have been demonstrated.
Highlights
The solution of wave propagation phenomena in spatially discrete method for the numerical simulation always requires the elimination of the spurious events
The appropriate artificial numerical boundaries can be applied to eliminate the effect of unnecessary spurious reflections in case of the numerical simulations of wave propagation phenomena problems
We focus on absorbing boundary conditions known as nonreflecting boundary conditions
Summary
The solution of wave propagation phenomena in spatially discrete method for the numerical simulation always requires the elimination of the spurious events. Givoli and Neta (2003) incorporated a finite difference scheme and proposed a non-reflecting boundary scheme for time-dependent wave problems in unbounded domains [7]. The proposed method can describe the energy propagation in case of outward direction only This method almost reduces reflected compressional waves in boundary. Reynolds (1978) developed a finite difference models that shows unwanted reflections are produced from the edges of boundary [13]. This happens due to use of boundary conditions modeled by Dirichlet or Neumann. A systematic method is presented through applying the set of absorbing boundary conditions These conditions are noticed to be able to eliminate the unnecessary boundary events. The applied absorbing boundary conditions would be able to reduce or absorb the reflecting effect by the boundaries thorough the outward-moving energy
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