Method for three-dimensional incompressible unsteady N-S equation finite element numerical solution

Abstract

The invention discloses a method for a three-dimensional incompressible unsteady N-S equation finite element numerical solution. First a mathematic splitting method is applied to split an N-S equation into a diffusion equation, a convection equation and a pressure correction equation, a first speed transition value at a (n+1) moment is obtained through diffusion equation calculation according to an initial value at an n moment value and boundary conditions, and then a second speed transition value at the (n+1) moment is worked out through the convection equation, a pressure value at the (n+1) moment is calculated according to a pressure Poisson equation, a speed value at the (n+1) moment is obtained according to the speed correction equation, a bearing reaction formula is adopted to calculate acting force of fluid on the boundary, finally whether a current time step reaches a simulation duration is judged; if the current time step reaches the simulation duration, computing is stopped, or else next-step time cycle computing is executed until the simulation duration is reached. A speed-pressure interpolation function does not need to meet LBB conditions, difficulty of weight function correction by finite elements is effectively avoided, and calculation efficiency is greatly improved.

Description

technical field [0001] The invention belongs to the technical field of fluid mechanics, and in particular relates to the design of a three-dimensional incompressible unsteady N-S equation finite element numerical solution method. Background technique [0002] Fluid flow is a common phenomenon in engineering practice. For example, in the fields of aviation, machinery, construction, power, hydraulics, chemical industry, energy, environment, biology and other engineering fields, there are a large number of problems related to fluid flow. In a sense, it is under the premise that the research on fluid mechanics issues has continuously achieved new results that has promoted the vigorous development of these engineering technology fields. [0003] Turbulent motion is a common phenomenon of fluid motion. The Navier-Stokes (N-S) equation is the basic control equation describing turbulent motion. It can essentially describe the law of fluid motion, such as atmospheric motion, ocean fl...

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Problems solved by technology

However, since the pressure interpolation function is one order lower than the velocity interpolation function, the velocity-pressure interpolation function cannot be chosen arbitrarily, and the convection equation is solved using the display method. At the same time, the time step is more demanding and the calculation cost is high.

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