SMOOTHING THE VELOCITIES IN MULTIDIMENSIONAL GAS-DYNAMIC CALCULATIONS WITH “D” CODES

A.Yu. Artemiev, Yu.D. Chernyshev
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 41-42.

      To suppress the short-wave velocity perturbations, the “D” codes [1] implement artificial viscosities of various types. For this purpose, the most efficient are contour and angular artificial viscosities. Furthermore, for highly 2-D flows an algorithm was developed and implemented on “D” codes for smoothing the normal velocity components at the interface. To some extent, the velocity smoothing algorithm is an analog of contour and angular viscosities. This algorithm is generalized to the inner points of domain where each family of the grid lines is considered as an interface during smoothing.
      For a uniform grid, Јhe smoothing operator has the first order approximation in time and third order approximation in space. To conserve the total energy, the kinetic energy transferred due to the velocity variations at the cell nodes is transformed to the internal energy. The pulse received by the grid node is transferred to the neighbors with inverted sign at the distance inversely proportional to the distance between the nodes.
      The smoothing algorithm proposed differs from the commonly used algorithms in that:
      — the timestep is explicitly included into the smoothing operator which makes the smoothing procedure relatively flexible (when the timestep size is reduced the complement to the velocity vanishes),
      — the smoothing is accomplished only for a given mode of angle variations in one of the families of the grid lines.
      This algorithm is generalized to the 3-D case and implemented in DF complex [2]. The complement to the velocity during the smoothing at the node represents a sum of complements obtained from the velocity smoothing on each of three surfaces passing through this node and determined by two families of grid lines.
      1. Dmitriev N.A., Dmiirieva L. V., Malinovskaya E. V., Sofronov I.D. A method for 2-D gas-dynamic nonstationary calculations in Lagrangian variables // Theoretical Fundamentals and Construction .of Numerical Algorithms for Computational Physics / Ed. by Babenko K.I. ?.: Nauka, 1979. P. 175-200.
      2. Artemiev A. Yu., Delov V.L, Dmiirieva L. V. A method for the 3-D nonstationary gas-dynamic calculationsin Lagrangian variables // Voprosy Atomnoy Nauki i Tekhniki. Ser. Matematicheskoye Modelirovaniye Fizicheskikh Protsessov. 1989. N 1. P. 30-39.