Title:	Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods
Authors:	Levý, Tomáš May, Georg
Citation:	Applied and Computational Mechanics. 2022, vol. 16, no. 2, p. 119-134.
Issue Date:	2022
Publisher:	University of West Bohemia
Document type:	článek article
URI:	http://hdl.handle.net/11025/50896
ISSN:	1802-680X (Print) 2336-1182 (Online)
Keywords:	hybridizovaná diskontinuální Galerkinova metoda;časově závislé problémy konvekce-difúze-reakce;vzorce zpětné diferenciace;diagonálně implicitní metoda Runge-Kutta;přizpůsobení velikosti časového kroku
Keywords in different language:	hybridized discontinuous Galerkin method;time-dependent convection-diffusion-reaction problems;backward differentiation formulas;diagonally implicit Runge-Kutta method;time step size adaptation
Abstract in different language:	The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely backward differentiation formulas (BDF) and diagonally implicit Runge-Kutta (DIRK) methods. Special attention is devoted to embedded DIRK methods, which allow the incorporation of time step size adaptation algorithms in order to keep the computational effort as low as possible. The properties of the numerical solution, such as its order of convergence, are investigated by means of suitably chosen test cases for a linear convection-diffusion-reaction equation and the nonlinear system of Navier-Stokes equations. For problems considered in this work, the DIRK methods prove to be superior to high-order BDF methods in terms of both stability and accuracy.
Rights:	© University of West Bohemia
Appears in Collections:	Články / Articles (KME) Volume 16, number 2 (2022) Volume 16, number 2 (2022)

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