On a compact finite-difference scheme of the third order of weak approximation

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Abstract

The stability and accuracy of compact difference schemes with artificial viscosities of the fourth divergence order are studied. These schemes have a third order both of classical approximation on smooth solutions and weak approximation on discontinuous solutions. As a result of the stability analysis of these schemes in the linear approximation, the optimal values of their viscosity coefficients were obtained. Test calculations are presented to demonstrate the advantages of the new compact scheme compared to the TVD and WENO schemes when calculating discontinuous solutions with shock waves.

Original languageEnglish
Article number012072
Number of pages6
JournalJournal of Physics: Conference Series
Volume1359
Issue number1
DOIs
Publication statusPublished - 21 Nov 2019
Event4th All-Russian Scientific Conference Thermophysics and Physical Hydrodynamics with the School for Young Scientists, TPH 2019 - Yalta, Crimea, Ukraine
Duration: 15 Sep 201922 Sep 2019

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