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 ...

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