ON CONSTRUCTION OF WENO SCHEMES FOR HYPERBOLIC SYSTEMS ON UNSTRUCTURED MESHE

Goryunov Vladimir Aleksandrovich, Doctor of physical and mathematical sciences, professor, sub-department of experimental physics, Ogaryev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), gorval1934@mail.ru
Zhalnin Ruslan Viktorovich, Candidate of physical and mathematical sciences, associate professor, sub-department of applied mathematics, Ogaryev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), zhalnin@gmail.com
Peskova Elizaveta Evgen'evna, Assistant, sub-department of applied mathematics, Ogaryev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), lizanika@mail.ru
Tishkin Vladimir Fedorovich, Doctor of physical and mathematical sciences, professor, deputy director for reseach, Keldysh Institute of Applied Mathematics Russian Academy of Sciences (4 Miusskaya square, Moscow, Russia), office@keldysh.ru

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Background. Mathematical simulation of fluid and gas flows is reduced to solving the equations of the Euler system in areas of complicated geometry. Real flows are characterized by the appearance of gas dynamic discontinuities. It leads to the usage of numerical methods of high order accuracy. The purpose of this paper is to construct essentially non oscillatory high order scheme (WENO scheme) on unstructured meshes for gas dynamics equations; and to compare the obtained results with the numerical results using first-order accuracy.
Materials and methods. The basic idea of WENO scheme is linear combination of polynomials constructed by the ENO scheme. Weights in the linear combination depend on the smoothness of solution in each set. For treatment of negative weights the authors carried out disintegration thereof.
Results. The authors developed an essentially non oscillatory third-order scheme (WENO scheme) on unstructured meshes for gas dynamics equations. The obtained results were compared with the numerical results using first-order accuracy.
Conclusions. The researchers developed a third order scheme using a combination of linear polynomials. A series of test calculations for the Riemann problem using this scheme was performed. It is concluded that the proposed scheme smears the solutions on discontinuities less than the first order scheme.

WENO scheme, unstructured mesh, high-order accuracy.

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