APPLICATION OF METHOD OF CHARACTERISTIC DIRECTIONS WITH SEPARATION OF FLOW SINGULARITIES TO CALCULATION OF EQUATIONS OF GAS DYNAMICS WITH HEAT CONDUCTION

D.N. Bokov, N.N. Bokov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 45-46.

       The work major equations of characteristic directions method and algorithms for separation of strong and weak discontinuities. Peculiarities are discussed of solving hyperbolic components of system of equations describing invicid motion of heat conducting gas.
      A main dissimilarity from the wide known mesh-characteristic methods described in monograph [1] involves the fact that the solution is constructed on four independent mesh sets:
      - Eulerian observation mesh;
      - mesh of characteristics corresponding to eigennumber (u - α);
      - mesh of characteristics corresponding to eigennumber (u);
      - mesh of characteristics corresponding to eigennumber (u + α);
      The first set can be absend.
      The determining system of difference equations is written in the form of finite increments of conservative dependent variables along the characteristic directions. Such form of presenting solution doesn’t lead to appearance of limitations on time step of Currant condition type, and enables to track formation and evolution of strong discontinuities.
      Dissimilarity from the classical method of characteristics [2] is that arbitrary equations of state are considered and the mesh solution is constructed for one time. This enables to apply implicit methods, of solving parabolic components of the initial system of equations.
      1. Magomedov K.M., Kholodov A.S. Meshicharacteristic Numerical-Methods. M.: Nauka Publishers,; 1988.
      2. Zhukov A.I. Application of Method of Characteristics to Numerical Solution of One-Dimensional Problems of Gas Dynamics // Proceedings of MIAN USSR. I960. Vol. 58.