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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 discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). 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 unbounded flow past 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. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.
Original language | English |
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Article number | 164 |
Pages (from-to) | 1-32 |
Journal | Fluids |
Volume | 4 |
Issue number | 3 |
DOIs | |
Publication status | Published - 3 Sept 2019 |
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Dive into the research topics of 'An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations'. Together they form a unique fingerprint.Projects
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Biomechanics Meets Robotics: Methods for Accurate and Fast Needle Targeting
Wittek, A. (Investigator 01), Singh, S. (Investigator 02), Miller, K. (Investigator 03), Hannaford, B. (Investigator 04) & Fichtinger, G. (Investigator 05)
ARC Australian Research Council
1/01/16 → 31/03/22
Project: Research