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UBC Theses and Dissertations

A high-order accurate particle-in-cell method Edwards, Essex


We propose the use of high-order accurate interpolation and approximation schemes alongside high-order accurate time integration methods to enable high-order accurate Particle-in-Cell methods. The key insight is to view the unstructured set of particles as the underlying representation of the continuous fields; the grid used to evaluate integro-differential coupling terms is purely auxiliary. We also include a novel regularization term to avoid the accumulation of noise in the particle samples without harming the convergence rate. We include numerical examples for several model problems: advection-diffusion, shallow water, and incompressible Navier-Stokes in vorticity formulation. The implementation demonstrates fourth-order convergence, shows very low numerical dissipation, and is competitive with high-order accurate Eulerian schemes.

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