TY - JOUR
T1 - Conservative, high-order particle–mesh scheme with applications to advection-dominated flows
AU - Maljaars, Jakob M.
AU - Labeur, Robert Jan
AU - Trask, Nathaniel
AU - Sulsky, Deborah
PY - 2019
Y1 - 2019
N2 - By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation – locally and globally – and extending to high-order spatial accuracy. This is achieved via the introduction of a novel particle–mesh projection operator which casts the particle–mesh data transfer as a PDE-constrained optimization problem, permitting advective flux functionals at cell boundaries to be inferred from particle trajectories. This optimization problem seamlessly fits in a HDG framework, whereby the control variables in the optimization problem serve as advective fluxes in the HDG scheme. The resulting algebraic problem can be solved efficiently using static condensation. The performance of the scheme is demonstrated by means of numerical examples for the linear advection–diffusion equation and the incompressible Navier–Stokes equations. The results demonstrate optimal spatial accuracy, and when combined with a θ time integration scheme, second-order temporal accuracy is shown.
AB - By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation – locally and globally – and extending to high-order spatial accuracy. This is achieved via the introduction of a novel particle–mesh projection operator which casts the particle–mesh data transfer as a PDE-constrained optimization problem, permitting advective flux functionals at cell boundaries to be inferred from particle trajectories. This optimization problem seamlessly fits in a HDG framework, whereby the control variables in the optimization problem serve as advective fluxes in the HDG scheme. The resulting algebraic problem can be solved efficiently using static condensation. The performance of the scheme is demonstrated by means of numerical examples for the linear advection–diffusion equation and the incompressible Navier–Stokes equations. The results demonstrate optimal spatial accuracy, and when combined with a θ time integration scheme, second-order temporal accuracy is shown.
KW - Advection-dominated flows
KW - Conservation
KW - Finite element methods
KW - Hybridized discontinuous Galerkin
KW - Particle-in-cell
KW - PDE-constrained optimization
UR - http://www.scopus.com/inward/record.url?scp=85061641839&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2019.01.028
DO - 10.1016/j.cma.2019.01.028
M3 - Article
AN - SCOPUS:85061641839
SN - 0045-7825
VL - 348
SP - 443
EP - 465
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -