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Selective Damping in a Galerkin Method for Solving Wave Problems with Variable Grids

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  • 1 Department of Earth and Atmospheric Sciences, Saint Louis University, Saint Louis, Mo. 63103
  • | 2 Department of Mathematical Studies, Southern Illinois University, Edwardsville 62026
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Abstract

A dissipative Galerkin procedure is used to solve two hyperbolic problems on an irregular or variable grid. Both forced wave motions (Gaussian) and boundary induced wave propagations are considered. It is shown that results obtained by using the traditional Galerkin approximation can be improved by using the dissipative procedure. Reflections or noise produced an a grid because of mesh refinements can be substantially reduced by this technique. Comparisons are also made with the dissipative effects obtained from an added artificial viscosity term.

Abstract

A dissipative Galerkin procedure is used to solve two hyperbolic problems on an irregular or variable grid. Both forced wave motions (Gaussian) and boundary induced wave propagations are considered. It is shown that results obtained by using the traditional Galerkin approximation can be improved by using the dissipative procedure. Reflections or noise produced an a grid because of mesh refinements can be substantially reduced by this technique. Comparisons are also made with the dissipative effects obtained from an added artificial viscosity term.

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