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Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to compete with conventional mesh-based methods, high order accuracy is essential. The Local Anisotropic Basis Function Method (LABFM) is a mesh-free method introduced in King et al., J. Comput. Phys. 415:109549 (2020), which enables the construction of highly accurate difference operators on disordered node discretisations. Here, we introduce a number of developments to LABFM, in the areas of basis function construction, stencil optimisation, stabilisation, variable resolution, and high order boundary conditions. With these developments, direct numerical simulations of the Navier Stokes equations are possible at extremely high order (up to 10th order in characteristic node spacing internally). We numerically solve the isothermal compressible Navier Stokes equations for a range of geometries: periodic and channel flows, flows past a cylinder, and porous media. Excellent agreement is seen with analytical solutions, published numerical results (using a spectral element method), and experiments. The potential of the method for direct numerical simulations in complex geometries is demonstrated with simulations of subsonic and transonic flows through an inhomogeneous porous media at pore Reynolds numbers up to Re=968.
Mesh-free methods have significant potential for simulations in complex geometries, as the time consuming process of mesh-generation is avoided. Smoothed Particle Hydrodynamics (SPH) is the most widely used mesh-free method, but suffers from a lack o
In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approa
We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists
This work presents a new multiphase SPH model that includes the shifting algorithm and a variable smoothing length formalism to simulate multi-phase flows with accuracy and proper interphase management. The implementation was performed in the DualSPH
The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly-resolved direct numerical simulations of isotropic