In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to so...In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.展开更多
基金the European Union’s NextGenerationUE-Project:Centro Nazionale HPC,Big Data e Quantum Computing,“Spoke 1”(No.CUP E63C22001000006)E.Macca was partially supported by GNCS No.CUP E53C22001930001 Research Project“Metodi numericiper problemi differenziali multiscala:schemi di alto ordine,ottimizzazione,controllo”+1 种基金E.Macca and S.Boscarino would like to thank the Italian Ministry of Instruction,University and Research(MIUR)to supportthis research with funds coming from PRIN Project 2022(2022KA3JBA,entitled“Advanced numericalmethods for time dependent parametric partial differential equations and applications”)Sebastiano Boscarinohas been supported for this work from Italian Ministerial grant PRIN 2022 PNRR“FIN4GEO:forward andinverse numerical modeling of hydrothermalsystemsin volcanic regions with application to geothermal energyexploitation”(No.P2022BNB97).E.Macca and S.Boscarino are members of the INdAM Research groupGNCS.
文摘In this paper, we present two semi-implicit-type second-order compact approximate Tay-lor(CAT2) numerical schemes and blend them with a local a posteriori multi-dimensionaloptimal order detection (MOOD) paradigm to solve hyperbolic systems of balance lawswith relaxed source terms. The resulting scheme presents the high accuracy when applied tosmooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearlyfail-safe property in terms of ensuring the positivity. The numerical results obtained from avariety of test cases, including smooth and non-smooth well-prepared and unprepared initialconditions, assessing the appropriate behavior of the semi-implicit-type second order CAT-MOODschemes. These results have been compared in the accuracy and the efficiency witha second-order semi-implicit Runge-Kutta (RK) method.
