arXiv subjects

Dinshaw S. Balsara

Publications and source records attributed to Dinshaw S. Balsara.

51 records · Page 3Linked to original sources

arXiv2011

A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes.

physics.comp-ph↗

arXiv2010

Efficient Implementation of ADER Schemes for Euler and Magnetohydrodynamical Flows on Structured Meshes -- Comparison with Runge-Kutta Methods

ADER (Arbitrary DERivative in space and time) methods for the time-evolution of hyperbolic conservation laws have recently generated a fair bit of interest. The ADER time update can be carried out in a single step, which is desirable in many applications. However, prior papers have focused on the theory while downplaying implementation details. The purpose of the present paper is to make ADER schemes accessible by providing two useful formulations of the method as well as their implementation details on three-dimensional structured meshes. We therefore provide a detailed formulation of ADER schemes for conservation laws with non-stiff source terms in nodal as well as modal space along with useful implementation-related detail. We also provide details for the efficient use of ADER schemes in obtaining the numerical flux for conservation laws as well as electric fields for divergence-free magnetohydrodynamics. An efficient WENO-based strategy for obtaining zone-averaged magnetic fields from face-centered magnetic fields in MHD is also presented. The schemes catalogued here have been implemented in the first author's RIEMANN code. The speed of ADER schemes is shown to be almost twice as fast as that of strong stability preserving Runge-Kutta time stepping schemes for all the orders of accuracy that we tested.

physics.comp-ph↗

arXiv2010

Evaluating the Magnetorotational Instability's Dependence on Numerical Algorithms and Resolution

We have studied saturated, MRI-driven turbulence using three-dimensional, isothermal simulations with resolutions that extend from 64 to 192 zones in each direction. The simulations were performed with several higher order Godunov algorithms. A variety of reconstruction strategies as well as a variety of Riemann solvers are tried. We show that the details of the isothermal MRI-driven turbulence depend principally on the Riemann solver and secondarily on the reconstruction strategy. Furthermore, we find that the effective viscosity parameter parameter tends to show progressively smaller decrements with increasing resolution when the best reconstruction strategy (WENO) and the best Riemann solver (linearized)are used. We attribute this result to the more sophisticated dissipation mechanisms that are used in higher-order Godunov schemes. Spectral analysis and transfer functions have been used to quantify the dissipative processes in these higher-order Godunov schemes.

astro-ph.GA↗

arXiv2010

Direct Evidence for Two-Fluid Effects in Molecular Clouds

We present a combination of theoretical and simulation-based examinations of the role of two-fluid ambipolar drift on molecular line widths. The dissipation provided by ion-neutral interactions can produce a significant difference between the widths of neutral molecules and the widths of ionic species, comparable to the sound speed. We demonstrate that Alfven waves and certain families of magnetosonic waves become strongly damped on scales comparable to the ambipolar diffusion scale. Using the RIEMANN code, we simulate two-fluid turbulence with ionization fractions ranging from 10^{-2} to 10^{-6}. We show that the wave damping causes the power spectrum of the ion velocity to drop below that of the neutral velocity when measured on a relative basis. Following a set of motivational observations by Li & Houde (2008), we produce synthetic line width-size relations that shows a difference between the ion and neutral line widths, illustrating that two-fluid effects can have an observationally detectable role in modifying the MHD turbulence in the clouds.

astro-ph.GA↗

arXiv2009

Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows

In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by introducing a constant resolved state between the states being considered, which introduces sufficient dissipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver is proved to be positively conservative for the density variable; the positivity of the pressure variable has been demonstrated for Euler flows when the divergence in the fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow. We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical flows. A robust and efficient second order accurate numerical scheme for two and three dimensional Euler and magnetohydrodynamic flows is presented. The scheme is built on the current multidimensional Riemann solver. The number of zones updated per second by this scheme on a modern processor is shown to be cost competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps.

physics.comp-ph↗

arXiv2009

Simulations of the Boundary Layer Between a White Dwarf and its Accretion Disk

Using a 2.5D time-dependent axisymmetric numerical code we recently developed, we solve the full compressible Navier-Stokes equations (including an alpha-viscosity prescription) to determine the structure of the boundary layer between the white dwarf and the accretion disk in non-magnetic cataclysmic varia ble systems. In this preliminary work, our numerical approach does not include radiation. In the energy equation, we either take the dissipation function (Phi) into account or we assumed that the energy is instantly radiated away (Phi). For a slowly rotating non magnetized accreting white dwarf, the accretion disk e xtends all the way to the stellar surface. There, the matter impacts and spread s towards the poles as new matter continuously piles up behind it. We carried out numerical simulations for different values of the alpha viscosity parameter (alpha), corresponding to different mass accretion rates. In the high viscosity cases (alpha=0.1), the spreading boundary layer sets off a gravity wave in the s urface matter. The accretion flow moves supersonically over the cusp making it s usceptible to the rapid development of gravity wave and/or Kelvin-Helmholtz shea ring instabilities. This BL is optically thick and extends more than 30 degrees to either side of the disk plane after only 3/4 of a Keplerian rotation period (19s). In the low viscosity cases (alpha=0.001), the spreading boundary layer does not set off gravity waves and it is optically thin.

astro-ph↗

arXiv2008

Efficient, High Accuracy ADER-WENO Schemes for Hydrodynamics and Divergence-Free Magnetohydrodynamics

The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling the flow of neutral fluids and the divergence-free, ideal magnetohydrodynamics (MHD) system that is used for large scale modeling of ionized plasmas. Efficient techniques for weighted essentially non-oscillatory (WENO) interpolation have been developed for finite volume reconstruction on structured meshes. We also present a new formulation of the ADER (for Arbitrary Derivative Riemann Problem) schemes that relies on a local continuous space-time Galerkin formulation instead of the usual Cauchy-Kovalewski procedure. The schemes reported here have all been implemented in the RIEMANN framework for computational astrophysics. We demonstrate that the ADER-WENO meet their design accuracies. Several stringent test problems of Euler flows and MHD flows are presented in one, two and three dimensions. Many of our test problems involve near infinite shocks in multiple dimensions and the higher order schemes are shown to perform very robustly and accurately under all conditions.

physics.comp-ph↗

arXiv2008

Divergence-Free Reconstruction of Magnetic Fields and WENO Schemes for Magnetohydrodynamics

Balsara (2001, J. Comput. Phys., 174, 614) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD was shown in Balsara (2004, ApJS, 151, 149). Second order accurate divergence-free schemes for MHD have shown themselves to be very useful in several areas of science and engineering. However, certain computational MHD problems would be much benefited if the schemes had third and higher orders of accuracy. In this paper we show that the reconstruction of divergence-free vector fields can be carried out with better than second order accuracy. As a result, we design divergence-free weighted essentially non-oscillatory (WENO) schemes for MHD that have order of accuracy better than second. A multistage Runge-Kutta time integration is used to ensure that the temporal accuracy matches the spatial accuracy. Accuracy analysis is carried out and it is shown that the schemes meet their design accuracy for smooth problems. Stringent tests are also presented showing that the schemes perform well on those tests.

physics.comp-ph↗

arXiv2008

Dust Settling in Magnetorotationally-Driven Turbulent Discs I: Numerical Methods and Evidence for a Vigorous Streaming Instability

(Abridged) In this paper we have used the RIEMANN code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas in a vertically stratified protostellar accretion disc. The disc was modeled to have the density and temperature of a minimum mass solar nebula, and was driven to a fully-developed turbulence via the magnetorotational instability (MRI). We find that the inclusion of standard dust to gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution of the dust reaches a Gaussian profile, and the scale heights for the dust that we derive are shown to be proportional to the reciprocal of the square root of the dust radius. The largest dust shows a strong tendency to settle to the midplane of the accretion disc, and tends to organize itself into elongated clumps of high density. The dynamics of these clumps is shown to be consistent with a streaming instability. The streaming instability is seen to be very vigorous and persistent once it forms. Each stream of high density dust displays a reduced RMS velocity dispersion, and the densest clumpings of large dust are shown to form where the streams intersect. We have also shown that the mean free path and collision time for the dust that participates in the streaming instability is reduced by almost two orders of magnitude relative to the average mean free paths and collision times. We show that some of the large dust in our 10 au simulations should have a propensity for grain coalescence.

astro-ph↗

arXiv2008

A Two-Fluid Method for Ambipolar Diffusion

We present a semi-implicit method for isothermal two-fluid ion-neutral ambipolar drift that is second-order accurate in space and time. The method has been implemented in the RIEMANN code for astrophysical fluid dynamics. We present four test problems that show the method works and correctly tracks the propagation of MHD waves and the structure of two-fluid C-shocks. The accurate propagation of MHD waves in the two-fluid approximation is shown to be a stringent test of the algorithm. We demonstrate that highly accurate methods are required in order to properly capture the MHD wave behaviour in the presence of ion-neutral friction.

astro-ph↗

arXiv2006

Simulations of Mixed Morphology Supernova Remnants With Anisotropic Thermal Conduction

We explore the role of anisotropic thermal conduction on the evolution of supernova remnants through interstellar media with a range of densities via numerical simulations. We find that a remnant expanding in a dense environment can produce centre-bright hard x-ray emission within 20 kyr, and centre-bright soft x-ray emission within 60 kyr of the supernova event. In a more tenuous environment, the appearance of a centre-bright structure in hard x-rays is delayed until about 60 kyr. The soft x-ray emission from such a remnant may not become centre bright during its observable lifetime. This can explain the observations that show that mixed-morphology supernova remnants preferentially occur close to denser, molecular environments. Remnants expanding into denser environments tend to be smaller, making it easier for thermal conduction to make larger changes in the temperatures of their hot gas bubbles. We show that the lower temperatures make it very favorable to use high-stage ions as diagnostics of the hot gas bubbles in SNRs. In particular, the distribution of O VIII transitions from shell-bright at early epochs to centre-bright at later epochs in the evolution of an SNR expanding in a dense ISM when the physics of thermal conduction is included.

astro-ph↗

arXiv2006

Anisotropic Thermal Conduction in Supernova Remnants: Relevance to Hot Gas Filling Factors in the Magnetized ISM

We explore the importance of anisotropic thermal conduction in the evolution of supernova remnants via numerical simulations. The mean temperature of the bubble of hot gas is decreased by a factor of ~3 compared to simulations without thermal conduction, together with an increase in the mean density of hot gas by a similar factor. Thus, thermal conduction greatly reduces the volume of hot gas produced over the life of the remnant. This underscores the importance of thermal conduction in estimating the hot gas filling fraction and emissivities in high-stage ions in Galactic and proto-galactic ISMs.

astro-ph↗

arXiv2005

The accretion and spreading of matter on white dwarfs

For a slowly rotating non-magnetized white dwarf the accretion disk extends all the way to the star. Here the matter impacts and spreads towards the poles as new matter continuously piles up behind it. We have solved the 3d compressible Navier-Stokes equations on an axisymmetric grid to determine the structure of this boundary layer for different viscosities corresponding to different accretion rates. The high viscosity cases show a spreading BL which sets off a gravity wave in the surface matter. The accretion flow moves supersonically over the cusp making it susceptible to the rapid development of gravity wave and/or Kelvin-Helmholtz instabilities. This BL is optically thick and extends more than 30 degrees to either side of the disk plane after 3/4 of a Keplerian rotation period (t=19s). The low viscosity cases also show a spreading BL, but here the accretion flow does not set off gravity waves and it is optically thin.

astro-ph↗

arXiv2005

Simulating the boundary layer between a white dwarf and its accretion disc

We describe the results of numerical simulations of the dynamics of the boundary layer (BL) between the accretion disk and the surface of a non-magnetic white dwarf (WD) for different viscosities which corresponds to different stages for dwarf novae burst cycles. The simulations cover the inner part of the accretion disk, the BL, and the upper atmosphere of the star. The high viscosity case, which corresponds to a dwarf nova in outburst, shows a optically thick BL which after one Keplerian rotation period (t_K=19s) extends more than 30 degrees to either side of the disk plane. The BL is optically thick and thus occludes part of the star. The low viscosity case, which corresponds to a dwarf nova in quiescense, also shows a BL, but it is optically thin.

astro-ph↗

arXiv2005

The Distribution of Pressures in a Supernova-Driven Interstellar Medium. I. Magnetized Medium

Observations have suggested substantial departures from pressure equilibrium in the interstellar medium (ISM) in the plane of the Galaxy, even on scales under 50 pc. Nevertheless, multi-phase models of the ISM assume at least locally isobaric gas. The pressure then determines the density reached by gas cooling to stable thermal equilibrium. We use numerical models of the magnetized ISM to examine the consequences of supernova driving for interstellar pressures. In this paper we examine a (200 pc)^3 periodic domain threaded by magnetic fields. Individual parcels of gas at different pressures reach widely varying points on the thermal equilibrium curve: no unique set of phases is found, but rather a dynamically-determined continuum of densities and temperatures. A substantial fraction of the gas remains entirely out of thermal equilibrium. Our results appear consistent with observations of interstellar pressures. They also suggest that the high pressures observed in molecular clouds may be due to ram pressures in addition to gravitational forces. Much of the gas in our model lies far from equipartition between thermal and magnetic pressures, with ratios ranging from 0.1 to $10^4$ and ratios of uniform to fluctuating magnetic field of 0.5--1. Our models show broad pressure probability distribution functions with log-normal functional forms produced by both shocks and rarefaction waves, rather than power-law distributions produced by isolated supernova remnants. The width of the distribution can be described quantitatively by a formula derived from the work of Padoan, Nordlund, & Jones (1997).

astro-ph↗