{"title":"Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods","authors":"Tomáš Levý, G. May","doi":"10.24132/acm.2022.786","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24132/acm.2022.786","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Chemical Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The ACM journal covers a broad spectrum of topics in all fields of applied and computational mechanics with special emphasis on mathematical modelling and numerical simulations with experimental support, if relevant. Our audience is the international scientific community, academics as well as engineers interested in such disciplines. Original research papers falling into the following areas are considered for possible publication: solid mechanics, mechanics of materials, thermodynamics, biomechanics and mechanobiology, fluid-structure interaction, dynamics of multibody systems, mechatronics, vibrations and waves, reliability and durability of structures, structural damage and fracture mechanics, heterogenous media and multiscale problems, structural mechanics, experimental methods in mechanics. This list is neither exhaustive nor fixed.