عنوان انگلیسی مقاله:
A simplified Cauchy-Kowalewskaya procedure for the local implicit solution of generalized Riemann problems of hyperbolic balance laws
ترجمه فارسی عنوان مقاله:
یک روش ساده کوشی-کاوالووسکا برای راه حل ضمنی محلی از مشکلات ریمان تعمیم یافته قوانین تعادل hyperbolic
Sciencedirect - Elsevier - Computers and Fluids, 202 (2020) 104490: doi:10:1016/j:compfluid:2020:104490
Gino I. Montecinos a , ∗, Dinshaw S. Balsara b
The Cauchy-Kowalewskaya (CK) procedure is a key building block in the design of solvers for the Gen- eralised Riemann Problem (GRP) based on Taylor series expansions in time. The CK procedure allows us to express time derivatives in terms of purely space derivatives. This is a very cumbersome procedure, which often requires the use of software manipulators. In this paper, a simplification of the CK proce- dure is proposed in the context of implicit Taylor series expansion for GRP, for hyperbolic balance laws in the framework of [Journal of Computational Physics 303 (2015) 146-172]. A recursive formula for the CK procedure, which is straightforwardly implemented in computational codes, is obtained. The proposed GRP solver is used in the context of the ADER approach and several one-dimensional problems are solved to demonstrate the applicability and efficiency of the present scheme. An enhancement in terms of ef- ficiency, is obtained. Furthermore, the expected theoretical orders of accuracy are achieved, conciliating accuracy and stability.
Keywords: Finite volume schemes | ADER schemes | Generalized Riemann Problems | stiffsource terms