DIFFERENTIAL DISTANCE FUNCTION COMPUTATIONS FOR MESH GENERATION

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Essentially, distance functions (raw and modified nearest surface distances) are needed for RANS (Reynolds Averaged Navier-Stokes) turbulence modelling, general computational interface tracking for multiphase and free surface flows, electrostatic Coulomb force modelling and also flame front and explosion modelling along with ray tracing for optics and acoustics. They can also be used to capture Knudsen layer effects in microscale flows and for the implementation sponges and various other numerical wave reflection damping strategies and stabilising measures for LES (Large Eddy Simulation). Furthermore they can be used to implement hybrid LES-RANS strategies. Distance functions, can under certain circumstances be evaluated using expensive search operations. Alternatively, differential equations can be solved. Here, it is proposed to explore the solution of differential distance function equations on unstructured (where a wide range of cell shapes can be tessellated in a flexible fashion) moving and overset meshes to yield the above noted capabilities which are highly desirable for general purpose CFD codes. Flow solutions using such grids are increasingly common. However, robust mesh generation still presents a significant challenge. This is especially so if use is made of hexahedral cells and the higher numerical fidelity that they provide. Hence, here it is proposed to also explore the use of novel differential distance function related equation based approaches for: hybrid grid generation (hexahedral boundary layer cells linked to tetrahedral cells outside the boundary layer); pure hexahedral grid generation and overset grid computational interface location. The differential equations explored will include the hyperbolic Eikonal, Hamilton-Jacobi and elliptic Poisson. Especial attention will be paid to the economical and accurate solution of these equations on moving, unstructured over-set grids with mixed element topologies using finite element, finite volume & boundary element methods.