Grid method for solution of 2D Riemann type problem with two discontinuities having an initial condition | Zendy

Bahaddin Sinsoysal | Zendy; M. L. Rasulov | Zendy; Öykü YENER | Zendy

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Grid method for solution of 2D Riemann type problem with two discontinuities having an initial condition

Author(s) -

Bahaddin Sinsoysal,

M. L. Rasulov,

Öykü YENER

Publication year - 2021

Publication title -

bulletin of the karaganda university-mathematics

Language(s) - English

Resource type - Journals

eISSN - 2663-5011

pISSN - 2518-7929

DOI - 10.31489/2021m2/115-128

Subject(s) - riemann problem , classification of discontinuities , uniqueness , discontinuity (linguistics) , mathematics , initial value problem , cauchy problem , conservation law , mathematical analysis , exact solutions in general relativity , weak solution , riemann hypothesis , grid , type (biology) , geometry , ecology , biology

This study aims to obtain the numerical solution of the Cauchy problem for 2D conservation law equation with one arbitrary discontinuity having an initial profile. For this aim, a special auxiliary problem allowing to construct a sensitive method is developed in order to get a weak solution of the main problem. Proposed auxiliary problem also permits us to find entropy condition which guarantees uniqueness of the solution for the auxiliary problem. To compare the numerical solution with the exact solution theoretical structure of the problem under consideration is examined, and then the interplay of shock and rarefaction waves is investigated.

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