Mesh-Free Computational Fluid Dynamics
Mesh-free methods do not rely on any connectivity or mesh between computational nodes, unlike conventional mesh-based methods for computational mechanics. This feature eliminates difficult and time-consuming mesh generation. More importantly, the fully Lagrangian nature of these methods (in which the flow is tracked with moving virtual particles) facilitates some applications that are difficult for classical mesh-based Eulerian methods (where computational points are fixed in space). We are interested in Smoothed Particle Hydrodynamics (SPH) and other mesh-free methods as a means of simulating biomedical flow, in which blood often interacts strongly with moving structures such as elastic artery walls or the hinged leaflets of an artificial heart valve.
NUI, Galway is a member of SPHERIC, the SPH European Research Interest Group.
Dr. Nathan Quinlan, Marty Lastiwka, Mihai Basa, Ruairi Nestor, Rory Sweeney
We are working to understand and develop the numerical performance of two meshfree methods, Smoothed Particle Hydrodynamics (SPH) and the Finite Volume Particle Method (FVPM). The uiltimate goal is to apply these methods to problems in biomedical fluid dynamics with complex geometry and fluid-structure interaction, which are difficult to solve with conventional methods.
SPH is based on the use of a (usually bell-shaped) kernel function to approximate gradients of variables (such as pressure) from data is known at neighbouring nodes or particles. The kernel is analgous to the shape function in finite element method, but does not require connectivity between particles.
The principle of the SPH kernel function.
An important test case for computational models of viscous flow is the driven cavity, a 2D square chamber in which flow is driven by the sliding of the top wall. A sample SPH solution is shown below ( SPHERIC benchmark 3).Colouring corresponds to speed and the black curves are streamlines. The lid is driven from left to right.
SPH solution for flow in a lid-driven cavity.
SPH simulation of flow over a cylinder with vortex shedding
We have developed a technique analagous to mesh adaptation for distributing particles to improve accuracy in regions of high gradients. This yields an improvement in accuracy compared with standard SPH, for minimal additional computational cost, as shown below.
3D computations of nominally 1D shock tube flow for standard SPH (top) and SPH with adaptive particle distribution (bottom).
Nestor RM, Basa M, Lastiwka M, Quinlan NJ (2008) Extension of the finite volume particle method to viscous flow, Journal of Computational Physics 228(5):1733-1749.
Quinlan NJ, Basa M, Lastiwka M (2006) Truncation error in mesh-free particle methods, International Journal of Numerical Methods in Engineering 66(13):2064-2085.
Lastiwka M, Quinlan N, Basa M (2005) Adaptive particle distribution for Smoothed Particle Hydrodynamics, International Journal of Numerical Methods for Fluids 47(10–11):1403–1409.
This work is supported by an IRCSET Embark Scholarship to Ruairi Nestor and by IRCSET Basic Research Grant SC/02/189.