Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations

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• 作者：S. Busto^a ; ^{saray.busto@usc.es" class="auth_mail" title="E-mail the corresponding author} ; E.F. Toro^b ; ^{eleuterio.toro@unitn.it" class="auth_mail" title="E-mail the corresponding author} ; M.E. Vá ; zquez-Cendó ; n^a ; ^{elena.vazquez.cendon@usc.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Advection&ndash ; diffusion&ndash ; reaction equations ; Finite volume method ; ADER approach ; MUSCL-Hancock method ; Local truncation error ; Linear stability ; Empirical convergence rates
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：327
• 期：Complete
• 页码：553-575
• 全文大小：2119 K

文摘

We construct, analyze and assess various schemes of second order of accuracy in space and time for model advection–diffusion–reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial problems and are derived following two related approaches, namely ADER and MUSCL-Hancock. Detailed analysis of linear stability and local truncation error are carried out. In addition, the schemes are implemented and assessed for various test problems. Empirical convergence rate studies confirm the theoretically expected accuracy in both space and time.