Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

Abstract

We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame motion is adjusted to minimize local fluid velocities. Such approach allows to accommodate very efficiently large degrees of change in the flow extent. Moreover, by excluding the contribution of the bulk flow to the total energy the method eliminates the high Mach number problem in the flows of interest. An important practical advantage of the method is that it can be easily implemented with virtually any implicit or explicit Eulerian hydrodynamic scheme and adaptive mesh refinement (AMR) strategy.We also consider in detail equation invariance and existence of conservative formulation of equations for special classes of expanding/contracting reference frames. Special emphasis is placed on extensive numerical testing of the method for a variety of reference frame motions, which are representative of the realistic applications of the method. We study accuracy, conservativity, and convergence properties of the method both in problems which are not its optimal applications as well as in systems in which the use of this method is maximally beneficial. Such detailed investigation of the numerical solution behavior is used to define the requirements that need to be considered in devising problem-specific fluid motion feedback mechanisms.

Theoretical treatment of fluid flow for accelerating bodies

“…Poludnenko and Khokhlov [24] required a simulation system for astrophysics and cosmology which would be suitable for cases where the typical flow speeds are very much larger than the sound speed or the local flow velocities, in, for example, stellar cores or galactic formation. The inviscid equations are derived using a transformation into a non-inertial rotating frame with scaling factors in time, space, and density for this purpose.…”

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

“…We observe that the density is close to zero nearby the explosion center and the temperature is very high. The GRP scheme does it quite well, compared to the Godunov scheme, even to those in [27,24,26].…”

“…The Noh problem and the Sedov-Taylor problem have exact solutions [6,25,29] so that there are explicit illustrations about the performance of the present scheme. The analysis and simulations of explosion and implosion problems can be found in [27,24,26,9,10,13,18,23,30] and references therein. We can compare to show our results are competitive.…”

From Supernova to Supernova Remnant: The Three-dimensional Imprint of a Thermonuclear Explosion

“…We detail here the transformation that makes the computational grid co-expand with the SNR, without any need to add grid cells or refinement layers. The technique is commonly used for cosmological simulations, it was applied to SNRs by Fraschetti et al (2010), following Poludnenko & Khokhlov (2007). 9 Everywhere in this section tilde quantities refer to transformed quantities, i.e.…”