scholarly journals First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

2014 ◽  
Author(s):  
Alireza Mazaheri ◽  
Hiroaki Nishikawa
Keyword(s):  
Hyperbolic System ◽  
Time Dependent ◽  
First Order ◽  
Advection Diffusion ◽  
System Method ◽  
Diffusion Problems

scholarly journals Solution of Time-dependent Advection-Diffusion Problems with the Sparse-grid Combination Technique and a Rosenbrock Solver

2001 ◽  
Vol 1 (1) ◽  
pp. 86-98 ◽  
Author(s):  
Boris Lastdrager ◽  
Barry Koren ◽  
Jan Verwer
Keyword(s):  
Time Integration ◽  
Size Control ◽  
Sparse Grid ◽  
Time Dependent ◽  
Step Size ◽  
Combination Technique ◽  
Burgers Equations ◽  
Advection Diffusion ◽  
Grid Approach ◽  
Diffusion Problems

Abstract In the current paper the efficiency of the sparse-grid combination tech- nique applied to time-dependent advection-diffusion problems is investigated. For the time-integration we employ a third-order Rosenbrock scheme implemented with adap- tive step-size control and approximate matrix factorization. Two model problems are considered, a scalar 2D linear, constant-coe±cient problem and a system of 2D non- linear Burgers' equations. In short, the combination technique proved more efficient than a single grid approach for the simpler linear problem. For the Burgers' equations this gain in efficiency was only observed if one of the two solution components was set to zero, which makes the problem more grid-aligned.

scholarly journals NUMERICAL ANALYSIS OF THE PSI SOLUTION OF ADVECTION–DIFFUSION PROBLEMS THROUGH A PETROV–GALERKIN FORMULATION

2007 ◽  
Vol 17 (11) ◽  
pp. 1905-1936 ◽  
Author(s):  
TOMÁS CHACÓN REBOLLO ◽  
MACARENA GÓMEZ MÁRMOL ◽  
GLADYS NARBONA REINA
Keyword(s):  
Splitting Schemes ◽  
First Order ◽  
Convergence Error ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Analysis Technique ◽  
Fluctuation Splitting ◽  
Convection Dominated ◽  
Nonlinear Fluctuation ◽  
Diffusion Problems

In this paper we introduce an analysis technique for the solution of the steady advection–diffusion equation by the PSI (Positive Streamwise Implicit) method. We formulate this approximation as a nonlinear finite element Petrov–Galerkin scheme, and use tools of functional analysis to perform a convergence, error and maximum principle analysis. We prove that the scheme is first-order accurate in H1 norm, and well-balanced up to second order for convection-dominated flows. We give some numerical evidence that the scheme is only first-order accurate in L2 norm. Our analysis also holds for other nonlinear Fluctuation Splitting schemes that can be built from first-order monotone schemes by the Abgrall and Mezine's technique.

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

Sign in / Sign up

Export Citation Format

Share Document