An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

Abstract

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We compute the spatial derivatives using the Meshless Point Collocation (MPC) method. We verify the accuracy of the numerical scheme for commonly-used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and vortex shedding behind a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods.

Hydrodynamic modeling and performance analysis of bio-inspired swimming

“…One particular aspect of this effort is the presented numerical approach, which demonstrates the capability of combining explicit dynamics meshless point collocation using Discretization Corrected Particle Strength Exchange [23] with immersed boundary method to solve the vorticity stream-function formulation of the incompressible Navier-Stokes equations and compute the fluid forces around moving/deforming bodies.…”

“…We identify the key kinematics parameters for design enhancement of bio-inspired underwater vehicles in terms of thrust production. The objective of the present study is to extend the research on numerical simulations of bio-inspired swimming and contribute to the development and validation of a computational model of fluid flow around a deforming fish-like body by combining the newly developed meshless [23] and immersed boundary methods (at the Intelligent Systems for Medicine Laboratory of the University of Western Australia) and the numerical investigation of the impact of fish kinematics and morphology, namely undulatory body with and without caudal and pectoral fins, on the propulsive performance dictated by thrust force generation. The remainder of the paper is organized as follows.…”

Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

“…Global vorticity boundary conditions are more accurate, since both boundary and interior nodes are involved in their computation. In the present study, the DC PSE differential operators were applied for the computation of the vorticity boundary conditions [45,53]. In the DC-PSE-meshless collocation context, computing and imposing vorticity boundary conditions were considered as an interpolation problem.…”

Recent Numerical Advances in Fluid Mechanics

“…The article by Guilizzoni et al [9] investigates the impact of multiple synchronized drops into a deep pool. In their paper, Bourantas et al [10] put forth a strong form meshless point collocation method for solving the unsteady incompressible Navier-Stokes equations. Fakhari [11] considered to develop a wall model for large eddy simulations in simulating either the body fitted or immersed boundary problems.…”