An explicit semi-Lagrangian, spectral method for solution of Lagrangian transport equations in Eulerian-Lagrangian formulations

10/15/2019
by   Hareshram Natarajan, et al.
0

An explicit high order semi-Lagrangian method is developed for solving Lagrangian transport equations in Eulerian-Lagrangian formulations. To ensure a semi-Lagrangian approximation that is consistent with an explicit Eulerian, discontinuous spectral element method (DSEM) discretization used for the Eulerian formulation, Lagrangian particles are seeded at Gauss quadrature collocation nodes within an element. The particles are integrated explicitly in time to obtain an advected polynomial solution at the advected Gauss quadrature locations. This approximation is mapped back in a semi-Lagrangian fashion to the Gauss quadrature points through a least squares fit using constraints for element boundary values and optional constraints for mass and energy preservation. An explicit time integration is used for the semi-Lagrangian approximation that is consistent with the grid based DSEM solver, which ensures that particles seeded at the Gauss quadrature points do not leave the element's bounds. The method is hence local and parallel and facilitates the solution of the Lagrangian formulation without the grid complexity, and parallelization challenges of a particle solver in particle-mesh methods. Numerical tests with one and two dimensional advection equation are carried out. The method converges exponentially. The use of mass and energy constraints can improve accuracy depending on the accuracy of the time integration.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/21/2022

Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method

A discrete analysis of the phase and dissipation errors of an explicit, ...
research
05/18/2021

Generalized smoothed particle hydrodynamics with overset methods in total Lagrangian formulations

This study proposes a generalized coordinates based smoothed particle hy...
research
03/08/2020

Lagrangian schemes for Wasserstein gradient flows

This paper reviews different numerical methods for specific examples of ...
research
12/23/2019

LEoPart: a particle library for FEniCS

This paper introduces LEoPart, an add-on for the open source finite elem...
research
03/01/2019

A massively parallel semi-Lagrangian solver for the six-dimensional Vlasov-Poisson equation

This paper presents an optimized and scalable semi-Lagrangian solver for...
research
04/04/2018

Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions

We present three new semi-Lagrangian methods based on radial basis funct...
research
03/02/2020

A Hybrid Lagrangian-Eulerian Method for Topology Optimization

We propose LETO, a new hybrid Lagrangian-Eulerian method for topology op...

Please sign up or login with your details

Forgot password? Click here to reset