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ON A MODE OF IDEAL GAS PLANAR LAYER EXPANSION INTO VACUUM

V. E. Shemarulin, S. S. L'vova, Yu. V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc 2015. Вып.3. С. 46-63.

We have discovered and investigated in detail the class of exact solutions of the gas dynamic equations that describe the isentropic ideal gas expansion into vacuum, when the gas fills a finite-thickness plane layer, in the case of specifically preset initial distributions of gas-dynamic parameters at the adiabatic index of 3.
      As an example, the particular case with the zero gas initial velocity, while the initial density velocity, in accordance with quadratic law, turns into zero on the gas-vacuum interface. Characteristic features of the solution and its connection with the Legendre polynomial are highlighted. The obtained particular solution can be used for testing the techniques and programs for numerical solving the gas dynamics problems. The following specifics of a numerical method can be checked when this solution is used as a test: degree of the entropy preservation in isentropic flows, accuracy of the flows description in the vicinity of weak and strong discontinuities on the vacuum interfaces. Additional information on the numerical method accuracy can be obtained by the verification of main quality properties of exact solutions in numerical solution: immobility of sound points (weak discontinuity points), immobility of flow boundaries up to the known time, vacuum line movements (gradient catastrophe curves) under the known law.
      The results of the numerical solution for the problem in question obtained with the EGAK technique are presented.

Keywords: 1D gas dynamics equations, ideal gas, isentropic expansion into vacuum, exact solutions, numerical solution.








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