Numerical integration methods for the solution of Helmholtz equations with the Wave Based Technique

Regular paper

Philipp Zsifkovits

AVL List GmbH

Monday 1 june, 2015, 15:20 - 15:40

0.7 Lisbon (47)

The Wave Based Technique is a method for airborne noise simulation, which is aimed for applications in the low- and mid-frequency range. The main focus of this article is on application to sound radiation of internal combustion engines. The discretization of the Helmholtz equation, which is the basis for the Wave Based Technique, requires the computation of certain surface integrals with high accuracy using numerical quadrature rules. Structural vibrations of a given surface (e.g. the surface of an engine block), have to be mapped to the integration points. With increasing frequency the number of integration points in these quadratures has to be increased to achieve the desired accuracy. Every time the integration points are increased the mapping procedure has to be done anew. To save computational time it is therefore desirable to reuse of the integration points and the already computed mapping information whenever this is possible. This paper demonstrates different strategies to reuse all or a subset of the integration points in order to increase the performance. The application of these strategies is benchmarked using a model of an inline 4-cylinder Diesel engine. An analysis of how the new strategies affect the simulation results is done and performance is compared to the straightforward approach in which no reuse of integration points is done.

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