Optimization Based Particle-Mesh Algorithm for High-Order and Conservative Scalar Transport

Conference paper (2020)

Authors

J.M. Maljaars Rivers, Ports, Waterways and Dredging Engineering - CEG
R.J. Labeur Environmental Fluid Mechanics - CEG
Nathaniel Trask Sandia National Laboratories, New Mexico
Deborah Sulsky University of New Mexico
Research Group
Rivers, Ports, Waterways and Dredging Engineering (CEG) (TU Delft)
Copyright: © 2020 J.M. Maljaars, R.J. Labeur, Nathaniel A. Trask, Deborah L. Sulsky
DOI: https://doi.org/10.1007/978-3-030-30705-9_23
Lagrangian-Eulerian Hybridized discontinuous Galerkin Conservation Advection equation Particle-mesh PDE-constraints
More Info
expand_more

Published Date

2020

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Civil Engineering & Geosciences

Department

Hydraulic Engineering

Research Group

Rivers, Ports, Waterways and Dredging Engineering

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.