Whole-flow-field simulation method of Hermite interpolation basic weighted non-oscillatory format

A technology of Hermitian interpolation and simulation methods, which is used in special data processing applications, complex mathematical operations, instruments, etc.

Inactive Publication Date: 2017-09-29
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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  • Abstract
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  • Application Information

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Problems solved by technology

[0004] Aiming at the deficiencies in the prior art, the present invention provides a full flow field simulation method based on Hermitian interpolation basic weighted non-oscillating format, wh

Method used

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  • Whole-flow-field simulation method of Hermite interpolation basic weighted non-oscillatory format
  • Whole-flow-field simulation method of Hermite interpolation basic weighted non-oscillatory format
  • Whole-flow-field simulation method of Hermite interpolation basic weighted non-oscillatory format

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Embodiment 1

[0197] Embodiment 1, step problem. This problem is a classic example proposed by Emery in 1968 to test the nonlinear hyperbolic conservation law scheme. The initial data is that the Mach number of the horizontal incoming flow is 3, the density is 1.4, the pressure is 1, the pipeline area is [0,3]′[0,1], and there is a step with a height of 0.2 at a distance of 0.6 from the left boundary, and the step extends to the end of the pipe. The upper and lower boundaries are reflection boundaries, the left boundary is the incoming flow boundary, and the right boundary is the outflow boundary. Figure 3a-3b and Figure 4a-4b Contour diagrams of density and pressure at time t=4 are given respectively.

Embodiment 2

[0198] Embodiment 2, the problem of double Mach reflection on inclined planes. The problem is to describe the changes that occur after a strong shock wave is incident on a slope at an angle of 30° to the plane. The incoming flow is a strong shock wave with a Mach number of 10. The calculation area takes [0, 3]'[0, 2], starting from The shock wave is perpendicular to the x-axis, and the initial data is:

[0199]

[0200] The left and right states are U L =(8,66.009,0,563.544) T , U R =(1.4,0,0,2.5) T , the boundary condition processing is that the left and right boundaries take the left and right state values ​​respectively. lower bound: when When , it is set as a reflective boundary; when , set to the left state. Upper boundary: when x>g(t), take the right state; when When , take the left state, where Figures 5a-5b and Figures 6a-6b Contour diagrams of density and pressure at time t=0.2 are given respectively.

Embodiment 3

[0201] Embodiment 3, the problem of flow around a cylinder. Considering that the supersonic inviscid fluid flows to a cylinder with a diameter of 1, the initial data is a horizontal incoming flow with a Mach number of 3, a density of 1, and a pressure of 1, and the calculation area is [-10, 10]? [10,10], the left boundary is the incoming flow boundary, and the right boundary is the supersonic outflow boundary. Figure 7a-7b and Figures 8a-8b The density and Mach number contours obtained by the two methods in the calculation area are given respectively.

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Abstract

The invention provides a whole-flow-field simulation method of the Hermite interpolation basic weighted non-oscillatory format. A finite-volume Robust HWENO format is constructed in the Cartesian coordinate, and through the cooperation with the immersed boundary method, a compressible flowing-around problem is calculated, the robustness of the Robust HWENO format is better than that of a HWENO format, and the Robust HWENO format is more easily popularized into a high-dimensional or movable and self-adaptive grid. Under a structural grid, when directly simulating the problem, the finite-volume Robust HWENO format requires a high-quality grid, however, generation of the high-quality grid is very complicated, and the immersed boundary method is a good method which can well process the boundary of an object surface and can be effectively used in various computational grids. Therefore, in the method, the finite-volume Robust HWENO format is effectively combined with the immersed boundary method, numerical simulation of the compressible flowing-around problem can be effectively conducted on a very simple Cartesian grid, and several numerical value simulation results of classical steady and unsteady problems fully verify the effectiveness of the method.

Description

technical field [0001] The invention discloses a full flow field simulation method based on Hermitian interpolation basic weighted non-oscillating format, and relates to the technical field of computational fluid mechanics engineering. Background technique [0002] In computational fluid dynamics numerical simulation, the construction and application of high-precision schemes have always been the focus of research, because high-precision schemes can accurately simulate the entire flow field, and can simulate the structure of the solution well and accurately capture the excitation. wave position. In 1983, Harten proposed the TVD (Total Variation Diminishing) format for the first time, and on this basis, he and Osher proposed the ENO (Essentially Non-Oscillatory) high-precision format in 1987. The main idea of ​​the ENO format is to expand the template successively. Select the smoothest template to construct a polynomial to obtain the value at the cell boundary, and then achi...

Claims

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Application Information

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IPC IPC(8): G06F17/50G06F17/13G06F17/12
CPCG06F17/12G06F17/13G06F30/23
Inventor 王镇明朱君赵宁
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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