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Full-flow-field simulation method based on central five-order WENO format of staggered grid

A simulation method and staggered grid technology, applied in special data processing applications, complex mathematical operations, instruments, etc., can solve the problems of unsatisfactory results of CWENO format examples, large amount of calculation, unsatisfactory simulation of complex flow fields, etc. Excellent numerical simulation effect, simple algorithm structure, high calculation accuracy effect

Inactive Publication Date: 2019-11-15
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Problems solved by technology

However, in the one-dimensional case, the CWENO format of these traditional central schemes is not ideal for some calculation examples, and the calculation amount is large; Simulation is also not ideal

Method used

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  • Full-flow-field simulation method based on central five-order WENO format of staggered grid
  • Full-flow-field simulation method based on central five-order WENO format of staggered grid
  • Full-flow-field simulation method based on central five-order WENO format of staggered grid

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specific Embodiment 1

[0069] Combined with two specific examples, the specific process of solving the one-dimensional and two-dimensional cases of the new form of the finite volume fifth-order WENO scheme mentioned in the present invention and the full flow field simulation method disclosed in the present invention will be described in detail below. .

[0070] One-dimensional structure:

[0071] Let the one-dimensional Euler equation be:

[0072] u t +f(U) x =0 (1)

[0073] Among them, U=(ρ,ρu,E) T Indicates a conserved variable, f(U)=(ρu,ρu 2 +p,u(E+p)) T , f(U) represents flux, U t Indicates that U is derived from t, f(U) x Indicates the derivation of f(U) with respect to x, ρ, p, u, E represent fluid density, pressure, horizontal velocity and energy respectively, and T represents transposition. Assuming that the grid cell step size is fixed, x i+1 / 2 -x i-1 / 2 =Δx=h, the grid center is Grid unit is I i =[x i-1 / 2 ,x i+1 / 2 ], where the subscript i is the coordinate number, x i The v...

specific Embodiment 2

[0184] The method disclosed in the present invention will be further described through ten calculation examples below.

[0185] Example 1

[0186] Tests on precision issues. We consider the one-dimensional Bugers equation:

[0187]

[0188] The initial value is u(x,0)=0.5+sin(πx), using periodic boundary conditions, Figure 5 The CWENO-ZQ algorithm and the CWENO-QS algorithm are respectively given when T=0.5 / π in L 1 with L ∞ Under the precision and error performance.

[0189] Calculation example two

[0190] Tests on precision issues. We consider the one-dimensional Euler equation

[0191] u t +f(U) x =0, (43)

[0192] Among them, U=(ρ,ρu,E) T Indicates a conserved variable, f(U)=(ρu,ρu 2 +p,u(E+p)) T , f(U) represents flux, U t Indicates that U is derived from t, f(U) x Indicates the derivative of f(U) with respect to x, ρ, p, u, E represent fluid density, pressure, horizontal velocity and energy respectively, and T represents transposition. The initial va...

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Abstract

The invention discloses a full-flow-field simulation method based on a central five-order WENO format of a staggered grid. The invention discloses a full-flow-field simulation method based on a five-order basic weighted oscillation-free format under a central framework. The full-flow-field simulation method comprises the following steps: reconstructing a variable unit mean value at a half point byadopting a finite volume five-order WENO format in a new form; discretizing the time integral term by using a Gauss quadrature formula to obtain a Gaussian node combination of flux with respect to time at the whole point of space; reconstructing a variable point value at the integral point; reconstructing a value of a derivative of the flux at an integer point; obtaining a Gaussian node of the flux with respect to time at the whole space point; combining the unit mean value variable at the half point with the Gaussian node of the flux with respect to time at the whole point of space to obtaina unit mean value at the half point of the next time layer; and sequentially iterating to obtain a numerical result of the flow field at the termination moment in the calculation area. According to the full-flow-field simulation method, better precision can be achieved; better capture discontinuity is achieved, and meanwhile, part of problems which cannot be solved by a traditional algorithm canbe simulated; and the double-Mach reflection problem and the step problem which cannot be well solved by a traditional algorithm under the two-dimensional condition are solved.

Description

technical field [0001] The invention relates to the technical field of computational fluid dynamics engineering, in particular to a method for simulating a full flow field based on a central fifth-order weighted intrinsically non-oscillating format based on a staggered grid. 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 the high-precision format can accurately simulate the entire flow field, it can well simulate the structure of the solution and accurately capture the shock 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 t...

Claims

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Application Information

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IPC IPC(8): G06F17/50G06F17/11
CPCG06F17/11
Inventor 崔生柱朱君
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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