New WENO (Weighted Essentially Non-oscillatory) format construction method under trigonometric function framework

A technology of trigonometric functions and construction methods, which is applied in complex mathematical operations, electrical digital data processing, special data processing applications, etc., and can solve problems such as difficult implementation and complex calculations

Active Publication Date: 2018-11-06
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

Zhu and Qiu proposed a method to reconstruct the WENO format with trigonometri...

Method used

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  • New WENO (Weighted Essentially Non-oscillatory) format construction method under trigonometric function framework
  • New WENO (Weighted Essentially Non-oscillatory) format construction method under trigonometric function framework
  • New WENO (Weighted Essentially Non-oscillatory) format construction method under trigonometric function framework

Examples

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Embodiment 1

[0112] 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 horizontal velocity is 3, the vertical velocity is 0, the pressure is 1, the pipeline area is [0,3]×[0,1], and the distance from the left boundary is 0.6 There is a step with a height of 0.2, 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 1a-1c The density contour plot at t=4 is given.

Embodiment 2

[0113] Embodiment 2, double Mach reflection problem. This problem describes the changes that occur when a strong shock wave at an angle of 60° to the x-axis hits a reflecting wall, and the incoming flow is a strong shock wave with a Mach number of 10. The calculation area is [0, 4] × [0, 1]. Region bottom from The reflective boundary condition starts at y=0, and the other bottom boundaries (from x=0 to That part) is the wavefront condition. Figure 2a-2c The density contour map in the [0,3]×[0,1] region is given at t=0.2.

Embodiment 3

[0114] Embodiment 3, the problem of mutual interference between shock wave and eddy current. The shock wave with a Mach number of 1.1 is located at x=0.5 and is perpendicular to the x-axis. The initial state of the shock wave is The small eddy is located to the left of the shock and its center is at (x c ,y c )=(0.25, 0.5). The eddy current can be regarded as the disturbance of the velocity, temperature and entropy of the mean flow, expressed as:

[0115]

[0116] where, τ=r / r c , ε=0.3, r c =0.05, α=0.204, γ=1.4, and the calculation area is [0, 2]×[0, 1]. Figures 3a-3c The pressure contour map in the [0,1]×[0,1] region is given at t=0.35. Figures 4a-4c The pressure contour map in [0.4, 1.45]×[0, 1] area at t=0.6 is given. Figures 5a-5c The pressure contour map in the [0,2]×[0,1] region is given at t=0.8.

[0117] Embodiment 4, two-dimensional Euler Riemann problem. The calculation area is [0, 1]×[0, 1], and the initial value conditions are respectively se...

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Abstract

The invention discloses a new WENO (Weighted Essentially Non-oscillatory) format construction method under a trigonometric function framework. Compared with a classic essentially non-oscillatory format constructed through utilization of an algebraic polynomial, a weighted essentially non-oscillatory format constructed through utilization of a trigonometric function polynomial has the advantage that the weighted essentially non-oscillatory format is easier to simulate wave or high frequency oscillation problems, can obtain high order numerical precision can be obtained in a smooth area, and keeps essentially non-oscillatory property at shock wave and contact discontinuity locations. Even if the new TWENO format and the classic five-order WENO format employ information at the same five points, according to the new TWENO format, the lower global L<1> and L<infinite> norm truncation errors can be obtained. According to linear weights employed by the new TWENO format, the optimum solutiondoes not need to be obtained through burdensome numerical calculation, the linear weights can be set as any positive numbers satisfying the fact that the sum is 1. Compared with the classic WENO format, the new TWENO format has the advantages that the new TWENO format is simpler, has higher robustness and is easier to popularize to a high-dimensional space. According to the new TWENO format, a plurality of classic Euler problems are effectively and numerically simulated, and the effectiveness is sufficiently verified.

Description

technical field [0001] The invention belongs to the technical field of computational fluid dynamics engineering, and in particular relates to a new WENO format construction method under the trigonometric function framework. Background technique [0002] Flow field problems often arise in engineering applications, such as aerodynamic systems and shallow water modeling. Therefore, developing robust, accurate, and efficient numerical simulation methods to solve such problems is of great importance and has attracted the interest of many researchers. In 1959, Godunov proposed a first-order precision numerical simulation scheme for solving flow field problems. The numerical simulation method with first-order accuracy will not cause non-physical numerical oscillations when capturing shock waves, but it will over-smooth strong discontinuities, and often strong discontinuities are of great significance to the follow-up research of the problem, so it is necessary to introduce high-pr...

Claims

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Application Information

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IPC IPC(8): G06F17/50G06F17/15
CPCG06F17/15G06F30/23G06F2111/10
Inventor 王延萌朱君熊良林
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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