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Steady-state Navier-Stokes equation solving method for automatically calculating optimal relaxation factor

A relaxation factor and automatic calculation technology, applied in design optimization/simulation, complex mathematical operations, CAD numerical modeling, etc., can solve problems such as unable to continue to decline, achieve the effect of ensuring calculation stability and improving convergence speed

Inactive Publication Date: 2020-06-16
磐芮信息科技(上海)有限公司
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Problems solved by technology

On this basis, the present invention also improves the actual use of the optimal relaxation factor, and mainly solves two problems: 1) Due to the drastic change of the flow field in the initial steps of the steady-state calculation, a smaller relaxation factor is required to ensure the calculation Stability; 2) If the relaxation of each step is continuously changing, it may cause the final residual to stabilize at a larger value and cannot continue to decline

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  • Steady-state Navier-Stokes equation solving method for automatically calculating optimal relaxation factor
  • Steady-state Navier-Stokes equation solving method for automatically calculating optimal relaxation factor
  • Steady-state Navier-Stokes equation solving method for automatically calculating optimal relaxation factor

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Embodiment

[0048] The method proposed by the invention is suitable for solving the steady-state Navier-Stokes equation. The Navier-Stoke equation is a partial differential equation. Here we take the finite volume discretization method as an example to show the numerical solution process. According to the flow of the algorithm, the partial differential equations involved in solving are mainly equation (1). Here we show how to discretize equation (1). Substituting the stress τ into equation (1) and sorting it out, the following equation is obtained:

[0049]

[0050] Using the finite volume method, the convection term Discrete as follows:

[0051]

[0052] where F=(U) f ·S f is the volume flow through the surface. It can be seen that the value U of the transported amount U on the surface needs to be calculated here f, which needs to be calculated through the discrete format of the convection term, commonly used formats include second-order upwind, QUICK, etc. Diffusion term ...

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Abstract

The invention discloses a steady-state Navier-Stokes equation solving method for automatically calculating an optimal relaxation factor in the technical field of fluid mechanics calculation, and the method comprises the following steps: 1, carrying out the finite volume discretization of a momentum equation, and obtaining an equation in a semi-discrete form; 2, using a relaxation factor for the equation in the semi-discrete form to obtain a relaxed equation; 3, solving the relaxed equation to obtain a predicted value of the speed, and constructing an intermediate speed; 4, constructing a pressure equation according to the continuity equation; 5, solving the pressure equation to obtain a pressure field, and relaxing the pressure field; 6, correcting the velocity field according to the relaxed pressure; and 7, solving a turbulence transportation equation, and updating the turbulence field. According to the method, error analysis is carried out based on a solving process of an SIMPLEC algorithm, and a formula of an optimal relaxation factor of a velocity field is derived. On the basis, the actual use of the optimal relaxation factor is improved. The improved process greatly improves the convergence rate on the premise of ensuring the calculation stability.

Description

technical field [0001] The invention relates to a method for solving the Navier-Stokes equation in the technical field of fluid dynamics calculation, in particular to a method for solving the steady-state Navier-Stokes equation with a faster convergence speed and automatic calculation of the optimal relaxation factor. Background technique [0002] Navier-Stokes equations (English name: Navier-Stokes equations), describe the motion equations of viscous incompressible fluid momentum conservation. It is called N-S equation for short. The equation of motion for viscous fluids was first proposed by Navier in 1827, which only considered the flow of incompressible fluids. Poisson proposed the equations of motion for compressible fluids in 1831. Saint-Venant in 1845 and Stokes independently proposed a form in which the viscosity coefficient is a constant in 1845, both of which are called the Navier-Stokes equation, or N-S equation for short. [0003] The flow process in a large c...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/12G06F17/13G06F30/23G06F111/10
CPCG06F17/12G06F17/13
Inventor 邱小平郭子锐吴凯健
Owner 磐芮信息科技(上海)有限公司
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