Optimization Based Particle-Mesh Algorithm for High-Order and Conservative Scalar Transport
Jakob M. Maljaars (TU Delft - Rivers, Ports, Waterways and Dredging Engineering)
Robert Jan Labeur (TU Delft - Environmental Fluid Mechanics)
Nathaniel A. Trask (Sandia National Laboratories, New Mexico)
Deborah L. Sulsky (University of New Mexico)
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Abstract
A particle-mesh strategy is presented for scalar transport problems which provides diffusion-free advection, conserves mass locally (i.e. cellwise) and exhibits optimal convergence on arbitrary polyhedral meshes. This is achieved by expressing the convective field naturally located on the Lagrangian particles as a mesh quantity by formulating a dedicated particle-mesh projection based via a PDE-constrained optimization problem. Optimal convergence and local conservation are demonstrated for a benchmark test, and the application of the scheme to mass conservative density tracking is illustrated for the Rayleigh–Taylor instability.