scholarly journals A research study on unsteady state convection diffusion flow with adoption of the finite volume technique

2021 ◽  
Vol 20 (4) ◽  
pp. 65-76
Author(s):  
Manoj R. Patel ◽  
Jigisha U. Pandya
Keyword(s):  
Finite Volume ◽  
Research Study ◽  
Unsteady State ◽  
Diffusion Flow ◽  
Convection Diffusion

scholarly journals A multilevel Monte Carlo finite difference method for random scalar degenerate convection–diffusion equations

2017 ◽  
Vol 14 (03) ◽  
pp. 415-454 ◽  
Author(s):  
Ujjwal Koley ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Franziska Weber
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Convergence Rate ◽  
Finite Volume ◽  
Monte Carlo Algorithm ◽  
Diffusion Equations ◽  
Entropy Solutions ◽  
Finite Volume Scheme ◽  
Multilevel Monte Carlo ◽  
Convection Diffusion

This paper proposes a finite difference multilevel Monte Carlo algorithm for degenerate parabolic convection–diffusion equations where the convective and diffusive fluxes are allowed to be random. We establish a notion of stochastic entropy solutions to these equations. Our chief goal is to efficiently compute approximations to statistical moments of these stochastic entropy solutions. To this end, we design a multilevel Monte Carlo method based on a finite volume scheme for each sample. We present a novel convergence rate analysis of the combined multilevel Monte Carlo finite volume method, allowing in particular for low [Formula: see text]-integrability of the random solution with [Formula: see text], and low deterministic convergence rates (here, the theoretical rate is [Formula: see text]). We analyze the design and error versus work of the multilevel estimators. We obtain that the maximal rate (based on optimizing possibly the pessimistic upper bounds on the discretization error) is obtained for [Formula: see text], for finite volume convergence rate of [Formula: see text]. We conclude with numerical experiments.

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