Meshless algorithm for supersonic inviscid gas flows calculating

DOI: 10.34759/trd-2021-119-04

Аuthors

Sposobin A. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: spise@inbox.ru

Abstract

The presented work regards the problem solution of numerical modeling of blunted body flow-around by the supersonic inviscid gas flow [1, 2]. Such problem may be solved by rather wide specter of the well-known methods. Cartesian-grid-based immersed boundary method was successfully applied to solve this problem in the two-dimensional setting [3, 4]. It was employed to study the flow evolution in the shock layer while large-size particle movement along the symmetry axis was performed within the framework of a series of works [5-7]. The above said studies continuation while a particle movement along various trajectories required the problem solution of the gas flow modeling in the 3D setting.

Unlike the finite volume method, the meshless method does not divide the computational domain into mesh cells, but uses the cloud of points to represent the values of functions. The least square method is being used for spatial approximation of function derivatives. The article describes the Harten-Lax-van Leer method in combination with the MUSCL scheme and Van Albada limiter as applied to Euler system solution in 3D space. The least square method is being used to approximate Neuman boundary conditions on the boundary of the surface [17].

The meshless method selection was stipulated by the possibility of gas flow modeling in the domains with complex geometry. This method is less fastidious to the computer memory compared with those on the Cartesian meshes, employed in the previous works [4-7].

The meshless method for Euler equations solving was adapted also to the 2D space for the flat and axisymmetric cases [14].

The software implementation of the described method is accomplished in the C++ programming language and employs the OpenMP parallelization technology [15, 16].

The series of computational experiments on the bodies flow-around by the supersonic flow was performed to test the method operation accuracy. The article describes in detail the problem of modeling the sphere flow-around by the inviscid gas flow at the incident flow Mach number of 3. The algorithm for the nodes set generation in the 3D space for the given problem is described. A good agreement with solutions obtained by the finite volume methods on Cartesian meshes [3] and reference data [21] is demonstrated.

The next stage in the development of the meshless method is supposed to be solution of the Navier-Stokes equations in order to simulate supersonic viscous flows.

Keywords:

numerical simulation, meshless method, Euler equation, supersonic flows-around of bodies

References

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