Reconstruction of finite volume solution for parameter-dependent linear hyperbolic conservation laws

06/18/2020
by   Marie Billaud-Friess, et al.
0

This paper is concerned with the development of suitable numerical method for the approximation of discontinuous solutions of parameter-dependent linear hyperbolic conservation laws. The objective is to reconstruct such approximation, for new instances of the parameter values for any time, from a transformation of pre-computed snapshots of the solution trajectories for new parameter values. In a finite volume setting, a Reconstruct-Transform-Average (RTA) algorithm inspired from the Reconstruct-Evolve-Average one of Godunov's method is proposed. It allows to perform, in three steps, a transformation of the snapshots with piecewise constant reconstruction. The method is fully detailed and analyzed for solving a parameter-dependent transport equation for which the spatial transformation is related to the characteristic intrinsic to the problem. Numerical results for transport equation and linear elastodynamics equations illustrate the good behavior of the proposed approach.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/24/2021

The FVC scheme on unstructured meshes for the two-dimensional Shallow Water Equations

The fluid flow transport and hydrodynamic problems often take the form o...
research
10/07/2021

Utilizing Time-Reversibility for Shock Capturing in Nonlinear Hyperbolic Conservation Laws

In this work, we introduce a novel approach to formulating an artificial...
research
07/02/2021

Cell-average based neural network method for hyperbolic and parabolic partial differential equations

Motivated by finite volume scheme, a cell-average based neural network m...
research
07/06/2022

Lax-Wendroff flux reconstruction method for hyperbolic conservation laws

The Lax-Wendroff method is a single step method for evolving time depend...
research
12/21/2022

Parallel kinetic schemes for conservation laws, with large time steps

We propose a new parallel Discontinuous Galerkin method for the approxim...
research
12/16/2019

Alsvinn: A Fast multi-GPGPU finite volume solver with a strong emphasis on reproducibility

We present the Alsvinn simulator, a fast multi general purpose graphical...
research
04/10/2020

Flux-corrected transport for scalar hyperbolic conservation laws and convection-diffusion equations by using linear programming

Flux-corrected transport (FCT) is one of the flux limiter methods. Unlik...

Please sign up or login with your details

Forgot password? Click here to reset