519.63 Two-dimensional method WENO9-SM-MP with a high Order of approximation for simulating flows with strong discontinuities

Belolutskiy F. A. (Institute for Computer Aided Design of the Russian Academy of Sciences), Shepelev V. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Fortova S. V. (Institute for Computer Aided Design of the Russian Academy of Sciences)

WENO, COMPUTATIONAL FLUID DYNAMICS, SHOCK WAVES, SYMMETRY-PRESERVING SCHEMES, SYMMETRY BREAKING, LOW DISSIPATION SCHEMES, RAYLEIGH—TAYLOR INSTABILITY


doi: 10.18698/2309-3684-2025-1-328


A generalization of the previously developed 9th-order WENO-SM-MP numerical scheme to two spatial dimensions is carried out with a procedure of its full symmetrization with respect to spatial dimensions. Verification of the scheme is conducted for problems of ideal gas dynamics. It is shown that the scheme is relatively low-dissipative and acceptably resolves 2D tests while being more efficient than the corresponding WENO-M, WENO-FM or WENO-ZM schemes of the same order with an MP limiter.


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Белолуцкий Ф.А., Шепелев В.В., Фортова С.В. Двумерный метод WENO9-SM-MP высокого порядка аппроксимации для расчёта течений с сильными разрывами. Математическое моделирование и численные методы, 2025, № 1, с. 3–28.


Работа выполнена при финансовой поддержке Министерства науки и высшего образования РФ (госзадание 124022400174-3).


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