Immersed boundary implicit iterative solving method meeting no-slip boundary conditions and continuity conditions

Abstract

The invention discloses an immersed boundary implicit iterative solving method meeting no-slip boundary conditions and continuity conditions; the method mainly comprises the steps of using a viscous incompressible flow N-S control equation, expanding a momentum equation along a feature line to perform time discretization, using a finite element method to perform spatial discretization, and adding additional body force to the discretized control equation; using a direct force method to solve the additional body force so that interpolation speed on the boundary is equal to expected speed distribution; when a fractional step method is in use, dividing the additional body force into two parts according to whether it is coupled to pressure, and solving the two parts respectively; performing speed correction in iterative computation of the additional body force and pressure to obtain final flow field distribution. The problem of an existing immersed boundary method that no-slip boundary conditions and continuity conditions cannot be met at same time is solved; after the additional body force is divided into two parts, the cost of solving a component item uncoupled to the pressure is effectively reduced, and the computing efficiency of the immersed boundary method is improved.

Description

technical field [0001] The invention relates to an implicit iterative solution method for immersed boundaries satisfying no-slip boundary conditions and continuity conditions, and belongs to the technical field of numerical solution of immersed boundary methods. Background technique [0002] In 1972, Peskin first proposed the immersed boundary method, and successfully applied it to biofluid mechanics to simulate the blood flow in human heart valves. The basic idea is to model the boundary of the structure as an additional body force in the Navier-Stokes momentum equation. A structured Cartesian grid is adopted, and two coordinate systems are used at the same time. The Euler coordinate system describes the flow field variables, and the Lagrange coordinate system describes the immersion boundary variables. [0003] When there are boundaries with complex shapes in the flow field, if the body-fitted mesh is used, the cost of generating the mesh is high. Using a Cartesian grid ...

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Problems solved by technology

[0006] In order to solve the deficiencies of the prior art, the object of the present invention is to provide an implicit iterative solution method for the immersed boundary that satisfies the no-slip boundary condition and the continuity condition, and solves the problem that the additional volume is not considered when solving the discrete fluid N-S equation in the prior art The problem that the coupling of force and pressure, the no-slip boundary condition and the continuity condition cannot be satisfied at the same time

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