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.
|Name||Lecture Notes in Computational Science and Engineering|
|Conference||19th International Conference on Finite Elements in Flow Problems, FEF 2017|
|Period||5/04/17 → 7/04/17|
- Advection equation
- Hybridized discontinuous Galerkin