An implicit boundary approach for viscous compressible high Reynolds flows using a hybrid remeshed particle hydrodynamics method

Abstract

We present an implicit boundary particle method with background mesh adaptation. We use a Brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high Reynolds numbers. A penalty term is added to the Navier-Stokes equations to impose the boundary conditions. The boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid, achieving diesel engine. The remeshed particle-mesh method coupled with Brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions.Many engineering applications require numerical simulations of viscous flows around complex geometries for which the body-fitted grid (BF) method [1], and the immersed boundary (IB) method [2, 3] are the two main approaches.The BF method proposes to generate grids associated with complex bound-5 aries. Consequently, boundary conditions are easily enforced. In order to achieve sufficiently accurate results for flows with high Reynolds numbers, a finer grid for the boundary layer is required. However, generating a good quality fine mesh can be cumbersome, and such meshes lead to substantial computational costs. In moving boundary cases, the simulation setup becomes more complex, 10 expensive as a result of the grid generation process, and the interpolation process of the solution to the new mesh at each computational time step creates projection errors. The BF method can thus be both complex to implement and computationally expensive. Peskin [4] introduced the IB method as a new approach to study the flow 15

Volume and Mass Conservation in Lagrangian Meshfree Methods

“…Without the ability to freely add and delete particles, particle distortion can not be fixed as easily in SPH type methods. Two common approaches are used for this: (i) redistributing particles based on a background mesh [41,42,43], or the more widely adopted (ii) artificially moving the particle cloud. For this, a non-physical or artificial movement of particles is performed to avoid particle clustering [32,33,45].…”

Point Cloud Generation for Meshfree Methods: An Overview

“…• Cartesian grids: The most common version of this is a Cartesian grid with uniformly distributed points in each dimension, giving a uniform cubic lattice [34,36,89,93,141,145,164,181].…”

Investigation of hydrodynamics of water impact and tail slamming of high-speed water entry with a novel immersed boundary method

“…The implicit scheme is also recommended since the boundary condition can be satisfied easily (Le et al. 2009; Obeidat & Bordas 2019; Yu & Pantano 2022). Different IB methods have their own advantages and disadvantages for flows with moving boundaries.…”

“…Yang et al (2009) and Gazzola et al (2011) recommended that the smooth discrete delta function be employed to avoid the spurious elastic effects and force oscillations mentioned above. The implicit scheme is also recommended since the boundary condition can be satisfied easily (Le et al 2009;Obeidat & Bordas 2019;Yu & Pantano 2022). Different IB methods have their own advantages and disadvantages for flows with moving boundaries.…”