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A Numerical Calculation Method of Finite Volume Flow Field Based on Non-equidistant Grid
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A finite volume, numerical calculation technology, applied in design optimization/simulation, special data processing applications, etc., can solve problems such as reduced accuracy, unstable format, negative linear weight, etc.
Active Publication Date: 2021-07-27
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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However, once it is extended to non-equidistant grids, its construction is relatively complicated, because its specific expressions are not only related to the physical quantities on the grid points but also related to the grid scale
In addition, whether it is an isometric grid or a non-isometric grid, the linear weight in the above process must be the optimal linear weight to make the overall format achieve the expected design accuracy, otherwise it will reduce the accuracy and even cause negative linear weights to cause the format unstable
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Embodiment 1
[0150] Embodiment 1, accuracy test problem. Considering the equation group (1), the initial conditions are: ρ(x,y,0)=1+0.2sin(π(x+y)), u(x,y,0)=0.7, v(x,y, 0)=0.3, p(x,y,0)=1. The exact solution is: ρ(x,y,t)=1+0.2sin(π(x+y-t)), u(x,y,t)=0.7, v(x,y,t)=0.3, p( x,y,t)=1. The calculation end time is t=2. The calculation area is (x,y)∈[0,2]×[0,2]. In order to illustrate that the linear weight in the numerical calculation method of the present invention can be arbitrarily selected, the present invention only takes five groups of numbers with different laws as the linear weight: (1) γ 1 =0.98,γ 2 =0.01,γ 3 =0.01; (2)γ 1 =0.495,γ 2 =0.495,γ 3 =0.01; (3)γ 1 =1 / 3,γ 2 =1 / 3,γ 3 = 1 / 3; (4)γ 1 =0.001,γ 2 =0.001,γ 3 =0.998; (5)γ 1 =0.3,γ 2 =0.4,γ 3 = 0.3.
[0151]
[0152]
[0153] Table 1 Comparison of the numerical accuracy of any five linear weights with the traditional WENO format
Embodiment 2
[0154] Embodiment 2, double Mach reflection problem. Such as figure 2 , image 3 As shown, there is a strong shock wave with a Mach number of 10 at 1 / 6 of the left boundary, which is injected at an angle of 60° with the x-axis, and the left and right state values are: (ρ L ,u L ,v L ,E L )=(8,7.145,-4.125,563.544), (ρ R ,u R ,v R ,E R )=(1.4,0,0,2.5). The number of CFL is 0.6, the calculation grid is 300×100, and the end time t=0.2.
Embodiment 3
[0155] Embodiment 3, radial symmetric Riemann problem. Such as Figure 4 As shown, considering the fluid dynamics equations (1), the initial conditions are:
[0156]
[0157] The calculation area is [0,1]×[0,1], the number of CFL is 0.6, the calculation grid is 100×100, and the calculation termination time is t=0.13.
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Abstract
A numerical calculation method for finite volume flow field based on non-equidistant grids, which involves a fifth-order finite volume WENO scheme with linear weights. Without reducing the overall numerical accuracy, only three additive A positive number equal to 1 is used as a linear weight, and then subsequent calculations can be performed. Since the numerical format constructed by the present invention does not need to calculate complex linear weights related to the grid scale under non-equidistant grids, it is easier to extend to higher-order WENO schemes, moving grids, or flow fields in adaptive grids calculate. In addition, the present invention, like the traditional WENO format, uses the Runge-Kutta time-discrete method with good stability, simple operation and easy programming to solve the problem. Finally, the present invention verifies its superiority in flow field calculation by comparing it with the traditional formula through specific numerical examples.
Description
technical field [0001] The invention discloses a finite volume flow field numerical calculation method based on non-equidistant grids, which can be used in computational mathematics, aerodynamics, magnetohydrodynamics, aerospace, missile launching, automobile industry, civil engineering, environmental engineering, ships , meteorological engineering and other technical fields. Background technique [0002] In recent decades, the high-order numerical solution format of hyperbolic conservation law equations has been the key research content, and its application fields include computational fluid dynamics, computational astronomy, semiconductorsimulation, traffic flow models, and magnetohydrodynamics. The main difficulty in solving the equations of these problems lies in the complexity of the solution. Even if the initial value is smooth, it will evolve over a period of time to produce complex solution structures such as shock waves, contact gaps, and sparse waves. In addition...
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