Meshfree methods for computational fluid dynamics

Non-smooth kernels for meshfree methods in fluid dynamics

A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton–Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are deriv...

Variational Methods for Computational Fluid Dynamics

Parallel extrapolation methods for computational fluid dynamics

Iterative solution methods for large, sparse linear systems of equations usually require significantly less time and memory than direct methods, and so are important in solving the systems which often arise in computational fluid dynamics. There are a number of eztrapolation algorithms which have been closely studied in the past as methods of accelerating convergence of iterative processes [3]....

Time Marching Kernel Approximated PDE Solutions for Meshfree Computational Fluid Dynamics

This paper will address the problem of time marching function approximated solutions inherent in emerging meshfree Computational Fluid Dynamics (CFD) solution techniques. The numerical solutions of partial differential equations (PDEs) of CFD has been dominated by either finite difference methods (FDM), finite element methods (FEM), and finite volume methods (FVM). These methods can be derived ...

The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics

In this paper we describe the repeated replacement method (RRM), a new meshfree method for computational fluid dynamics (CFD). RRM simulates fluid flow by modeling compressible fluids' tendency to evolve towards a state of constant density, velocity, and pressure. To evolve a fluid flow simulation forward in time, RRM repeatedly "chops out" fluid from active areas and replaces it with new "flat...