EFFECT OF THE WAY TO ACCOUNT FOR HEAT TRANSFER ON THE CALCULATION STABILITY OF TWO-PHASE GAS-DYNAMIC DIFFERENCE SCHEME
VANT. Ser.: Mat. Mod. Fiz. Proc 2015. Вып.3. С. 3-19.
The two-phase difference gas-dynamic scheme in Lagrangian variables is studied with account for heat transfer. We have discovered that the conditions for the Courant-type time-step strongly depend on the way the implicit heat conductivity is used in the difference scheme. In major cases the condition of stability is determined by the isentropic speed of sound. We offer a modification with account for the implicit heat conductivity in two energy equations. Continuous transition from the isentropic speed of sound to the isothermal one at the Courant thermal number increase is present in the conditions of the modified scheme stability.
The isothermal speed of sound is always less than the isentropic one, and when the radiation pressure is taken into account in the case of low densities and high temperatures, it can be several tens and hundreds times smaller than the isentropic one. Therefore in the modified scheme, with big Courant number, the time stem can increase significantly. Keywords: gas dynamics with thermal conductivity, difference schemes, splitting in terms of physical processes, difference scheme stability, isentropic speed of sound, isothermal speed of sound, thermal sound dispersion.
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