Regularized Smoothed Particle Hydrodynamics: A New Approach to Simulating Magnetohydrodynamic Shocks

Børve, S.; Omang, M.; Trulsen, J.

doi:10.1086/323228

Cited by 123 publications

(150 citation statements)

References 17 publications

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“…(21) by an adaptive anisotropic kernel function with tensor smoothing lengthes which are not fixed but evolved according to specific equations to follow the mean particle spacing as it varies in time, space, and direction around each particle. The particle regularization technique [4] and the similar one called re-meshing (or re-initialization) [5] can also be considered. Yet, it is an open problem how to design suitable regularization or re-meshing techniques in the presence of free surface as in case of a deforming drop.…”

Section: Drop Stretchingmentioning

confidence: 99%

Improved SPH methods for simulating free surface flows of viscous fluids

Fang

Parriaux

Rentschler

et al. 2009

Applied Numerical Mathematics

130

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In this paper we present two enhanced variants of the smoothed particle hydrodynamics (SPH) method for the numerical simulation of free surface flows of viscous fluids. Improvements are achieved by deriving a new set of general discrete SPH-like equations under an energy-based framework and applying a corrected (high-order) or coupled particle approximation scheme for function derivatives. By doing so, we ensure that the enhanced variants retain the conservative nature of SPH which is important for the stability of long-term simulations. Among various corrected approximations, we here implement the one obtained by the so-called finite particle method (FPM) within the framework to produce a higher-order SPH method which conserves both linear and angular momentums. In order to improve the efficiency of the higher-order variant, a coupled approach with the idea of using the SPH approximation for the interior particles and the FPM approximation for the exterior particles is also proposed and tested in this paper. Three prototype tests concerning free deformation of a viscous fluid patch with free surface are presented with comparisons between different methods to demonstrate the performance of the two proposed methods. Numerical results show that both the higher-order version using FPM and the coupled version using FPM/SPH outperform the original version of SPH in respect of accuracy and stability.

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Section: Drop Stretchingmentioning

confidence: 99%

Improved SPH methods for simulating free surface flows of viscous fluids

Fang

Parriaux

Rentschler

et al. 2009

Applied Numerical Mathematics

130

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“…However it turns out that the consistent formulation of the vector potential force has similar -in fact, much worse -problems with the tensile instability than even the standard conservative SPMHD force. Whilst we have managed to obtain reasonable results on a range of numerical tests with the consistent vector potential equations of motion, we find that a better approach is to use the vector potential in conjunction with a stable but non-conservative force such as those employed in Paper III and Børve et al (2001). The main practical improvement in this paper is therefore in the formulation of the dissipative terms.…”

Section: Introductionmentioning

confidence: 91%

“…In this paper, we stabilise the vector potential formulation we use the method proposed by Børve et al (2001), namely adding the "source term" −B(∇ · B)/ρ to the (conservative) force, giving…”

Section: Instability Correctionmentioning

confidence: 99%

“…In Paper II we have furthermore derived the equations of motion accounting for terms related to the smoothing length gradients which are necessary for exact simultaneous conservation of both energy and entropy. There is also a reasonable consensus on good approaches to removing the tensile instability in SPMHD, using either formulations proposed by Morris (1996) or by Børve, Omang & Trulsen (2001) which forgo the exact conservation of momentum slightly in order to attain numerical stability, the latter method simply by subtracting off the term in the force equation which is proportional to the non-zero divergence. Application of the Monaghan (2000) fix for the tensile instability (Paper I) turned out to be unsuccessful in compressible flows (Price 2004).…”

Section: Introductionmentioning

confidence: 99%

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Smoothed Particle Magnetohydrodynamics: Some Shocking Results

Price¹,

Monaghan

2004

Astrophysics and Space Science

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In this paper we investigate the use of the vector potential as a means of maintaining the divergence constraint in the numerical solution of the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. We derive a self-consistent formulation of the equations of motion using a variational principle that is constrained by the numerical formulation of both the induction equation and the curl operator used to obtain the magnetic field, which guarantees exact and simultaneous conservation of momentum, energy and entropy in the numerical scheme. This leads to a novel formulation of the MHD force term, unique to the vector potential, which differs from previous formulations. We also demonstrate how dissipative terms can be correctly formulated for the vector potential such that the contribution to the entropy is positive definite and the total energy is conserved.On a standard suite of numerical tests in one, two and three dimensions we find firstly that the consistent formulation of the vector potential equations is unstable to the well-known SPH tensile instability, even more so than in the standard Smoothed Particle Magnetohydrodynamics (SPMHD) formulation where the magnetic field is evolved directly. Furthermore we find that, whilst a hybrid approach based on the vector potential evolution equation coupled with a standard force term gives good results for one and two dimensional problems (where dA z /dt = 0), such an approach suffers from numerical instability in three dimensions related to the unconstrained evolution of vector potential components. We conclude that use of the vector potential is not a viable approach for Smoothed Particle Magnetohydrodynamics.

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“…However it would be fair to say that there was no real consensus on a standard approach and that many problems remained. Børve, Omang & Trulsen (2001) suggested an alternative to Morris' stabilisation based on explicitly subtracting the non-zero source term (-B∇·B) that is the cause of the stability problems in the momentum-conserving formulation. They also proposed a regularisation scheme for the SPH particle distribution which, though complicated, was found to give excellent results on MHD shock problems by the focussing of resolution where it is needed.…”

Section: A Prehistory Of Mhd In Sphmentioning

confidence: 99%

Magnetic fields and Turbulence in Star Formation using Smoothed Particle Hydrodynamics

Price

2010

Proc. IAU

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Abstract. Firstly, we give a historical overview of attempts to incorporate magnetic fields into the Smoothed Particle Hydrodynamics method by solving the equations of Magnetohydrodynamics (MHD), leading an honest assessment of the current state-of-the-art in terms of the limitations to performing realistic calculations of the star formation process. Secondly, we discuss the results of a recent comparison we have performed on simulations of driven, supersonic turbulence with SPH and Eulerian techniques.

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Regularized Smoothed Particle Hydrodynamics: A New Approach to Simulating Magnetohydrodynamic Shocks

Cited by 123 publications

References 17 publications

Improved SPH methods for simulating free surface flows of viscous fluids

Improved SPH methods for simulating free surface flows of viscous fluids

Smoothed Particle Magnetohydrodynamics: Some Shocking Results

Magnetic fields and Turbulence in Star Formation using Smoothed Particle Hydrodynamics

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