Spline-based meshing techniques for industrial applications

Abstract

Isogeometric Analysis (IgA) has become an accepted framework for the mod-elling, simulation and optimization (MSO) of engineering processes. However, the fully automatized generation of analysis-suitable parameterizations of geometries as they arise in practical workflows is still a challenging task, which often requires application-specific parameterization approaches. In this article we present a practical approach [6] based on the principles of Elliptic Grid Generation (EGG) for the efficient on-demand generation of analysis-suitable spline-based parameterizations. Starting from a (point cloud) description of the boundary provided by the existing MSO-pipeline, an inverse nonlinear Poisson-type problem is solved to obtain a folding-free (planar) parameterization of the entire domain. The non-linearity is efficiently treated with a globalized hierarchical Newton approach. Automatized boundary contour reparameterization techniques are employed to improve the parametric properties from a numerical viewpoint, such as orthogonal isolines and equally-sized cells. The use of curved instead of straight-sided elements allows us to arrive at an accurate description of the target domain with fewer elements and thus potentially lower computational effort. Numerical experiments with screw-compressor geometries demonstrate that the proposed algorithm reliably produces high-quality parameterizations typically within 3−4 Newton-iterations, even in the presence of extreme aspect-ratios. This makes it particularly attractive for the on-demand application within an automatized industrial MSO-pipeline. To support the demands of modern high-performance computing hardware, only a moderate number of sufficiently large and structured patches is generated which can be mapped one-by-one to the different devices (CPUs/GPUs) with only little communication overhead. Topology changes are avoided in time-dependent and shape-optimization settings. Finally, the spline-based geometry description can be transformed into a classical mesh by performing a large number of function evaluations in the mapping operator. Its continuous nature allows for feature-based (structured and unstructured) refinement and arbitrary element densities without increasing the complexity of the meshing process.