Speaker
Description
The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless transient velocity-vorticity formulation of the Navier-Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions. The false transient approach is utilised to improve stability.
As all boundary element methods, the Boundary-Domain Integral Method has a quadratic complexity. Here, the H2-methodology is applied to obtain an almost linear complexity. This acceleration technique is not only applied to the boundary part but more important to the domain related part of the formulation, ie to approximate the matrix related to the domain integrals. The strong singular integrals and the integral free term appearing in boundary element formulations are often solved indirectly by utilising the rigid body movement. This is not possible for formulations based on the H2-methodology because the matrix is never established. Here, it is shown how to apply the technique of Guigiani and Gigante to handle the strongly singular integrals.
The presented examples are a lid-driven cavity, Hagen-Poiseuille flow and the flow around a rigid cylinder. In the latter example the behaviour of the method for an unstructured grid is presented. Also the Reynolds number was increased to such a value that a transient numerical simulation has been performed. All examples show that the proposed method results in an almost linear complexity as the mathematical analysis promisses.
