M. Omang

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

Smoothed particle hydrodynamics (SPH) has proven to be a useful numerical tool in studying a number of different astrophysical problems. Still, used on other problems, such as the modeling of low-β MHD systems, the method has so far not performed as well as one might have hoped. The present work has been motivated by the desire to accurately model strong hydrodynamic and magnetohydrodynamic shocks, and a key issue has therefore been to achieve a near-optimal representation of the simulated system at all times. Using SPH, this means combining the Lagrangian nature of the method with a smoothing-length profile that varies in both space and time. In this paper, a scheme containing two novel features is proposed. First, the scheme assumes a piecewise constant smoothing-length profile. To avoid substantial errors near the steps in the profile, alternative forms of the SPH equations of motion are used. Second, a predictive attitude toward optimizing the particle distribution is introduced by activating a mass, momentum, and energy conservation regularization process at intervals. The scheme described has been implemented in a new code called regularized smoothed particle hydrodynamics (RSPH), and test results for a number of standard hydrodynamic and magnetohydrodynamic tests in one and two dimensions using this code are presented.

SPH in spherical and cylindrical coordinates

New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH. The Lagrangian formalism is used to derive the corresponding set of modified SPH equations of motion. The results show good agreement both with analytical and numerical results, in the case of the Sod shock tube test, the Noh infinite shock problem, and the Sedov point explosion test. The formulation has also been included in a 3D cylindrically symmetric problem of two colliding spherical shocks. For this latter problem, the results are presented allowing both a constant and a variable resolution. The results clearly demonstrate the capability of the new formulation to solve the singularity problem at the symmetry axis.

TWO-DIMENSIONAL MHD SMOOTHED PARTICLE HYDRODYNAMICS STABILITY ANALYSIS

Smoothed particle hydrodynamics (SPH) is an N-body integration scheme widely used within the field of astrophysics. Unfortunately, the method has up until recently been facing serious problems concerning instabilities when applied to MHD problems. Regularized smoothed particle hydrodynamics (RSPH) was proposed as an extension to SPH with the aim of achieving high-accuracy modeling of hydrodynamic and magnetohydrodynamic problems. This work included a new formulation of the discrete MHD equations that is easily implemented into SPH and RSPH codes alike. In this paper, the stability properties of two-dimensional linear MHD waves using this formulation are investigated. The presented analysis shows that linear stability properties similar to that obtained for sound waves in the absence of a magnetic field is achieved also for MHD waves. This result is confirmed by the included test results using both standard SPH and RSPH.

Multidimensional MHD shock tests of regularized smoothed particle hydrodynamics

This paper investigates to what extent the numerical scheme regularized smoothed particle hydrodynamics (RSPH) is able to accurately describe multidimensional MHD shocks. The scheme can be viewed as an extension to smoothed particle hydrodynamics (SPH), which is widely used for astrophysical applications. In the first of two previous papers, the basic idea behind the RSPH scheme was introduced and tested, primarily on one-dimensional MHD shock problems. A new formulation of the momentum equation was also proposed to secure stability in the low-β regime. A two-dimensional, linear stability analysis of this formulation was presented in the second paper. The second paper also utilized recent developments of the RSPH scheme that improve the overall description of multidimensional problems in general. Based on the results from the linear stability analysis, adjustments to the momentum equation are made in the present work, which are also applicable to the nonlinear regime. These adjustments address the problem of asymmetries in the momentum equation, which in nonlinear problems can lead to small, yet systematic errors in postshock conditions. In addition, this paper describes the first application of the improved RSPH scheme to multidimensional MHD shocks. Comparisons are made with existing methods, in particular the related SPH method. Special attention is given to the schemes ability to maintain the ∇ = 0 constraint and to what extent redefining the particle distribution affects the conservation of kinetic energy and angular momentum.

Shock Ignition of Reactive Particles

In this paper we study shock ignition of reactive particles in a shock tube environment. When shock propagates through a dust cloud consisting of reactive particles, the cloud is shifted, compressed, and the internal cloud temperature increased. In most experimental studies a closed-end shock tube is used to allow the shock to reflect and propagate through the cloud a second time, further increasing the dust particle temperature. We use a multi-phase version of the numerical Regularized Smoothed Particle Hydrodynamics (RSPH) method [1], to study shock ignition, and discuss important parameters that affect the particle ignition process.

Modelling high explosives (HE) using smoothed particle hydrodynamics

In this paper we present results from numerical simulations of high explosives, using a constant volume method and an axis-symmetric Regularized Smoothed Particle Hydrodynamics method. smoothed particle hydrodynamics method Empirical and numerical results show satisfactory agreement for 1 kg of detonating TNT charge. The method is further challenged with the study of shock propagation and shock reflection in complex geometries. The shock reflection pattern is altered by introducing barriers of different shapes. The effect of such barrier structures are studied.

Blast type shock wave phenomena simulated using regularized smoothed particle hydrodynamics

The numerical method RSPH is used to simulate shock reflection phenomena. In the first case we look at a shock colliding with a complex wedge configuration, whereas in the second case, the wedge is replaced by a square box. Our numerical results are found to be in good agreement with published experimental data. Reflection pattern and the pressure force on the box is studied for both short and long duration shock waves. The results demonstrate the capabilites of RSPH to handle shock reflection phenomena.

SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile

Concerns regarding efficiency and accuracy of Smoothed Particle Hydrodynamics (SPH) compared to modern grid-based methods have been raised. Likewise, the extension of SPH to MHD problems has proven to be a challenge. In an attempt to improve the ability of SPH to treat shocks in general, and MHD shocks in particular, a modified version of SPH called Regularized Smoothed Particle Hydrodynamics (RSPH) has been presented [1]. This method allows a piecewise constant smoothing length profile to be used. Furthermore, the smoothing length profile is optimized at temporal intervals using a mass, momentum and internal erergy conserving regularization process. In this paper, we examine more closely the abilities of the RSPH method to treat MHD shocks. We present a simple stability analysis, as well as results from MHD shock tests in one and two dimensions.