High order difference schemes using the local anisotropic basis function method

King, Jack; Lind, Steven; Nasar, Abouzied

doi:10.1016/j.jcp.2020.109549

Cited by 13 publications

(27 citation statements)

References 48 publications

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“…Recently, a new boundary treatment has been developed [38] with higher order capabilities (at least, for pressures). It should be noted as well that there is additional research on other high-order mesh-free methods such as the Local Anisotropic Basis Function Method (LABFM) [39] that interestingly collapses to SPH in the limiting low order case.…”

Section: Introductionmentioning

confidence: 99%

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

Antona

Vacondio

Avesani

et al. 2021

Water

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This paper studies the convergence properties of an arbitrary Lagrangian–Eulerian (ALE) Riemann-based SPH algorithm in conjunction with a Weighted Essentially Non-Oscillatory (WENO) high-order spatial reconstruction, in the framework of the DualSPHysics open-source code. A convergence analysis is carried out for Lagrangian and Eulerian simulations and the numerical results demonstrate that, in absence of particle disorder, the overall convergence of the scheme is close to the one guaranteed by the WENO spatial reconstruction. Moreover, an alternative method for the WENO spatial reconstruction is introduced which guarantees a speed-up of 3.5, in comparison with the classical Moving Least-Squares (MLS) approach.

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Section: Introductionmentioning

confidence: 99%

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

Antona

Vacondio

Avesani

et al. 2021

Water

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show abstract

“…With this motivation, in [17] we introduced the Local Anisotropic Basis Function method (LABFM) -a novel mesh-free method for generating high order spatial derivative operators. Derivative operators are constructed from the weighted sum (over the computational stencil) of field value differences, where the weights are obtained from a linear combination of anisotropic basis functions (ABFs).…”

Section: Introductionmentioning

confidence: 99%

“…The method was applied to a range of prototypical PDEs, and a simple unbounded incompressible flow problem, showing convergence up to 8 th order. We provided a detailed overview of the state of the art in mesh-free methods in [17], to which we refer interested readers. Compared with other mesh-free methods, LABFM provides much greater accuracy than Smoothed Particle Hydrodynamics (SPH), which in typical use (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we build on [17] and introduce two new developments that greatly increase the generality of LABFM. These are (i) new stabilisation techniques for dissipation of high wavenumber numerical instabilities (a common issue in all high order collocated schemes) and (ii) high order boundary conditions for complex geometries, including noslip, inflow, and outflow conditions.…”

Section: Introductionmentioning

confidence: 99%

“…By adding a small amount of hyperviscosity to the governing equations, the generation of high wavenumber modes can be suppressed, with minimal effect on the (low wavenumber) physical components of the flow. In [17] we followed this approach with LABFM to enable solutions of Burgers' equation at higher Reynolds numbers. In this work stabilisation is achieved through filtering variables at each time step and has yielded a robust procedure capable of stabilising simulations across a range of flows without the need for parameter tuning.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)

King,

Lind

2021

Preprint

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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 meshfree 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 10 th 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 Rep = 968.

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RKPM-based smoothed GFEM with Kronecker-Delta property for 2D and 3D solid problems

2022

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High order difference schemes using the local anisotropic basis function method

Cited by 13 publications

References 48 publications

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)

RKPM-based smoothed GFEM with Kronecker-Delta property for 2D and 3D solid problems

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