Open AccessGrid 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 -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
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) , initial value problem , mathematics , cauchy problem , conservation law , exact solutions in general relativity , weak solution , mathematical analysis , grid , riemann hypothesis , geometry
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.