Simulation of incompressibleparticle-based fluid flow inspiredby optimal transport

Sammanfattning

The simulation of particle-based fluid flow is usually compressible (∇·⃗ U̸ = 0) due to non-constantdensity, finite speed of sound from interaction effects, and lack of a global pressure field, which issolved in most cases via a Poisson equation. Therefore, solving a system with applicable imposedconstraints is usually numerically expensive. The goal of this thesis is to formulate a new methodfor fluid dynamics simulations that relies on particle-based dynamics, includes viscosity, and aglobal (grid-based) pressure-field optimizer to enforce incompressible flow conditions. The aimof this implementation is to allow topological independence for such problems as space filling.Specific uses arising from this are homogenization flows, since membranes and constrictions areeasily modeled in a particle-structure formulation, and mixtures of different density fluids. This method was implemented by discretization of the fluid flow into orthogonal occupation andvelocity grids and considering time stepping as a discrete assignment problem onto the grid.With the application of the Hungarian method to optimally solve the assignment problem, theincompressible Euler flow is approximated, with the optimal particle projection into the discretegrid being directly comparable to the pressure force enforcing incompressibility. The convergenceof this method is proven in a theoretically rigorous manner for the incompressible Euler equationin the mesh limit. The method, while on an orthogonal grid, is based fully on particle-based globaltransport and local viscosity calculations. Several tests and convergence studies were performedto confirm the applicability and precision of the method. A constricted channel, cylinder flow andKelvin-Helmholtz problem demonstrated the capability of the method in comparison to standardcodes and flow regimes. These showed the initial suitability of the method for simulating generalincompressible inviscid and viscous flow problems.