New Modification of 3d Meshless Lagrangian Vortex Method With Improved Boundary Condition Satisfaction and Divergence-Free Vorticity Representation

Abstract

A new approach is developed for incompressible 3D flow simulation around bodies by Lagrangian vortex method. Closed vortex loops are considered as vortex elements, which are generated on all the body surface and provide the satisfaction of the no-slip boundary condition. The procedure of double layer potential density reconstruction is considered, which consists of two steps. Firstly, the integral equation with respect to vortex sheet intensity is solved, which expresses the equality between the tangential components of flow velocity limit value and the body surface velocity. It is solved by using Galerkin approach. Secondly, the least-squares procedure is implemented, which permits to find nodal values of the double layer potential density. It is shown that the developed algorithm makes it possible to improve significantly the quality of solution for the bodies with very complicated geometry and low-quality surface meshes. The combination of this approach with vortex wake modelling with vortex loops, permits to simulate unsteady flows with higher resolution with acceptable numerical complexity. It can be useful for CFD applications and visual effects reproducing in computer graphics.

On the Algorithms for Vortex Element Evolution Modelling in 3D Fully Lagrangian Vortex Loops Method

“…It is proven in [7] that the vector integral equations and (2) is equivalent to its projection onto the tangential plane. Such approach (the T -scheme [8,9]) leads to the vector boundary integral equation of the 2-nd kind…”

“…In order to solve it numerically, the original semi-analytic approach, based on the Galerkin technique is developed, and its "keypoint" technique of the above mentioned surface improper integrals computation. This technique is described in details in [8,9,10].…”

Numerical Computation of Double Surface Integrals Over Triangular Cells for Vortex Sheet Intensity Reconstruction on Body Surface in 3d Vortex Methods

“… . In contrast to 2D case, when the exact analytic expressions can be derived [13] for all the coefficients of the linear system, which is an analogue of the system (8), for 3D case it is impossible to calculate the integrals in expressions (9), but it is possible to develop efficient semi-analytical algorithm [9]- [11], which provides rather high accuracy.…”