A Front Tracking Method for Conservation Laws with Boundary Conditions

1999 ◽  
pp. 493-502 ◽  
Author(s):  
K. Hvistendahl Karlsen ◽  
K.-A. Lie ◽  
N. H. Risebro
Keyword(s):  
Boundary Conditions ◽  
Conservation Laws ◽  
Front Tracking ◽  
Tracking Method ◽  
Front Tracking Method

scholarly journals Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method

2021 ◽  
Author(s):  
Adrian M Ruf
Keyword(s):  
Convergence Rate ◽  
Conservation Laws ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Stability Result ◽  
Front Tracking ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Discontinuous Flux ◽  
Scalar Conservation

Abstract We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in $u$ and the spatial dependency is piecewise constant with finitely many discontinuities. We use this stability result to prove a convergence rate for the front tracking method—a numerical method that is widely used in the field of conservation laws with discontinuous flux. To the best of our knowledge, both of these results are the first of their kind in the literature on conservation laws with discontinuous flux. We also present numerical experiments verifying the convergence rate results and comparing numerical solutions computed with the front tracking method to finite volume approximations.

A fully adaptive front tracking method for the simulation of two phase flows

2014 ◽  
Vol 58 ◽  
pp. 72-82 ◽  
Author(s):  
M.R. Pivello ◽  
M.M. Villar ◽  
R. Serfaty ◽  
A.M. Roma ◽  
A. Silveira-Neto
Keyword(s):  
Front Tracking ◽  
Two Phase Flows ◽  
Two Phase ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Fully Adaptive

Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

2016 ◽  
Vol 9 (1) ◽  
pp. 73-91 ◽  
Author(s):  
Haitian Lu ◽  
Jun Zhu ◽  
Chunwu Wang ◽  
Ning Zhao
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Front Tracking ◽  
Unstructured Meshes ◽  
Interfacial Region ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Medium Flow ◽  
Runge Kutta

AbstractIn this paper, we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible two-medium flow on unstructured meshes. A Riemann problem is constructed in the normal direction in the material interfacial region, with the goal of obtaining a compact, robust and efficient procedure to track the explicit sharp interface precisely. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

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