Ali Javed

An ALE based hybrid meshfree local RBF-cartesian FD scheme for incompressible flow around moving boundaries

A solution scheme is presented to simulate incompressible viscous flow around moving boundaries using hybrid meshfree-Cartesian grid. The presented solution approach avoids intensive re-meshing and enhances computational efficiency by combining the advantages of both meshfree and mesh-based methods for flow around moving objects. The scheme employs a body conformal meshfree nodal cloud around the solid object which convects with the moving solid boundary. On the outer side, meshfree nodal cloud is surrounded and partially overlapped by a stationary Cartesian grid. Navier Strokes equations in Arbitrary-Lagrangian-Eulerian (ALE) formulations are solved over moving nodal cloud using meshfree local Radial Basis Functions in finite difference Mode (RBF-FD). Eulerian form of flow equations are solved over static Cartesian grid using conventional finite difference scheme. Meshfree nodes can efficiently adapt to the moving boundary without necessitating re-meshing. Use of finite difference method over Cartesian grid allows faster computing and improves computational efficiency. Variation in computation time has been studied with corresponding change in size of meshfree and Cartesian grids. Significant reduction in computation time is achieved by reducing the size of meshfree cloud. The solution scheme is validated by simulating two dimensional flows around vibrating cylindrical objects. For this purpose, forced as well as vortex induced cylindrical vibration cases are investigated and solutions are compared with computational and experimental results available in literature.

Adaptive shape parameter (ASP) technique for local radial basis functions (RBFs) and their application for solution of navier strokes equations

The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not distributed uniformly throughout the domain. Unlike conventional approaches which assume globally similar values of RBF shape parameters, the presented ASP technique suggests that shape parameter be calculated exclusively for each data point (or node) based on the distribution of data points within its own influence domain. This will ensure interpolation accuracy while still maintaining well-conditioned system of equations for RBF weights. Performance and accuracy of ASP technique has been tested by evaluating derivatives and laplacian of a known function using RBF in Finite difference mode (RBFFD), with and without the use of adaptivity in shape parameters. Application of adaptive shape parameters (ASP) for solution of incompressible Navier Strokes equations has been presented by solving lid driven cavity flow problem on mesh-free domain using RBF-FD. The results have been compared for fixed and adaptive shape parameters. Improved accuracy has been achieved with the use of ASP in RBF-FD especially at regions where larger gradients of field variables exist.