Mesh curving for acoustic simulations with limited geometric knowledge

Abstract

High-order simulation techniques are advantageous for acoustic simulations. To effectively apply these methods, the domain geometry has also to be accurately described with high-order elements. In this thesis, mesh curving algorithms are considered under the restriction that only a fine linear target mesh is provided as input geometry. This situation can arise especially in the industrial context, where the original CAD data is not available, e.g. with scanned data or for a subcontracted simulation company.

Here, four mesh curving algorithms are described, one nodal method and three modal methods. Their applicability and curving accuracy is assessed and compared on basic geometries. This leads to a preselection of two modal methods which are then further tested for their influence on the simulation results for Helmholtz scattering problems. A modal curving that is based on the H¹-seminorm optimisation is selected as the more beneficial approach to curve meshes for acoustic simulations. It significantly reduces the geometrically induced field error compared to the other curving approaches. The chosen H¹ modal method is extended to 3D and applied to an academic and a realistic test case.

The second aspect of the thesis is the evaluation of the relation between the geometry discretisation error (GDE) and the field error that is induced by the geometric inaccuracy (GIE). This is first studied for the 2D Helmholtz scattering by a cylinder with nodal meshes obtained with the software Gmsh. Different measures are considered for the geometric accuracy and for the field error. The final model is described by an area based GDE and a field error evaluation along a ring in the simulation domain. It shows a linear relation between the GIE and GDE and a super-linear dependency of the frequency ω. Tests with modally curved meshes on the circular geometry and for the scattering by a distorted ellipse show that the considered GDE measure does not fully explain the dependency of the GIE on the geometric accuracy.

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Identifiers

ORCID for Alan Mcalpine: orcid.org/0000-0003-4189-2167

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