(Re-) Meshing using interpolative mapping and control point optimization

This work proposes a simple and fast approach for re-meshing the surfaces of smooth-featured geometries prior to CFD analysis. The aim is to improve mesh quality and thus the convergence and accuracy of the CFD analysis. The method is based on constructing an interpolant based on the geometry shape and then mapping a regular rectangular grid to the shape of the original geometry using that interpolant. Depending on the selected interpolation algorithm the process takes from less than a second to several minutes. The main interpolant discussed in this article is a Radial Basis Function with cubic spline basis, however other algorithms are also compared. The mesh can be optimized further using active (flexible) control points and optimization algorithms. A range of objective functions are discussed and demonstrated. The difference between re-interpolated and original meshes produces a metric function which is indicative of the mesh quality. It is shown that the method works for flat 2D surfaces, 3D surfaces and volumes.