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result(s) for
"gas dynamics"
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Fundamental solutions to the regularised 13-moment equations: efficient computation of three-dimensional kinetic effects
Fundamental solutions (Green’s functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier–Stokes–Fourier equations). Incorporation of these new fundamental solutions into a numerical framework based on the method of fundamental solutions (MFS) allows for efficient computation of three-dimensional gas microflows at remarkably low computational cost. The R13-MFS approach accurately recovers analytic solutions for low-speed flow around a stationary sphere and heat transfer from a hot sphere (for which a new analytic solution has been derived), capturing non-equilibrium flow phenomena missing from lower-order solutions. To demonstrate the potential of the new approach, the influence of kinetic effects on the hydrodynamic interaction between approaching solid microparticles is calculated. Finally, a programme of future work based on the initial steps taken in this article is outlined.
Journal Article
Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence
The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics
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is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.
Journal Article
A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics
We propose a low Mach number, Godunov-type finite volume scheme for the numerical solution of the compressible Euler equations of gas dynamics. The scheme combines Klein's non-stiff/stiff decomposition of the fluxes [J. Comput. Phys ., 121 (1995), pp. 213--237] with an explicit/implicit time discretization [F. Cordier, P. Degond, and A. Kumbaro, J. Comput. Phys. , 231 (2012), pp. 5685--5704] for the split fluxes. This results in a scalar second order partial differential equation (PDE) for the pressure, which we solve by an iterative approximation. Due to our choice of a crucial reference pressure, the stiff subsystem is hyperbolic, and the second order PDE for the pressure is elliptic. The scheme is also uniformly asymptotically consistent. Numerical experiments show that the scheme needs to be stabilized for low Mach numbers. Unfortunately, this affects the asymptotic consistency, which becomes nonuniform in the Mach number, and requires an unduly fine grid in the small Mach number limit. On the other hand, the CFL number is only related to the nonstiff characteristic speeds, independently of the Mach number. Our analytical and numerical results stress the importance of further studies of asymptotic stability in the development of asymptotic preserving schemes.
Journal Article
A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field
The study of the evolution of the atmosphere requires careful consideration of multicomponent gaseous flows under gravity. The gas dynamics under an external force field is usually associated with an intrinsic multiscale nature due to large particle density variation along the direction of force. A wonderfully diverse set of behaviors of fluids can be observed in different flow regimes. This poses a great challenge for numerical algorithms to accurately and efficiently capture the scale-dependent flow physics. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for a gas mixture is developed, which can be used for the study of cross-scale multicomponent flows under an external force field. The well-balanced scheme here indicates the capability of a numerical method to evolve a gravitational system under any initial condition to the hydrostatic equilibrium and to keep such a solution. Such a property is crucial for an accurate description of multicomponent gas evolution under an external force field, especially for long-term evolving systems such as galaxy formation. Based on the Boltzmann model equation for gas mixtures, the UGKS leverages the space–time integral solution to construct numerical flux functions and, thus, provides a self-conditioned mechanism to recover typical flow dynamics in various flow regimes. We prove the well-balanced property of the current scheme formally through theoretical analysis and numerical validations. New physical phenomena, including the decoupled transport of different gas components in the transition regime, are presented and studied.
Journal Article
Ficitious time integration method for solving the time fractional gas dynamics equation
In this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.
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Journal Article
A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas
In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems.
Journal Article
A Semi-Analytical Method to Investigate Fractional-Order Gas Dynamics Equations by Shehu Transform
This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an advantage over existing approaches because it does not require additional materials or computations. Four problems are used to test the authenticity of the proposed method. Using the suggested method, the solution proves to be more accurate. The proposed method can be implemented to solve many nonlinear fractional order problems because it has a straightforward implementation.
Journal Article
A discontinuous particle method for the inviscid Burgers' equation
The discontinuous particle method for simple problems associated with gas dynamics is under consideration. The origin of the method is based on the micro-model describing the movement of particles with prescribed velocities. We show that with the micro-model the inviscid Burgers' equation is solved in a weak sense. Numerical experiments have confirmed a low viscosity of the method: the solution is smeared by only one particle.
Journal Article
Solving Fractional Gas Dynamics Equation Using Müntz–Legendre Polynomials
To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniformly spaced meshes or the roots of shifted Legendre and Chebyshev polynomials. Müntz-Legendre polynomials have the interesting property that their fractional derivative is also a Müntz-Legendre polynomial. This property ensures that these bases do not face the problems associated with using the classical orthogonal polynomials when solving fractional equations using the collocation method. The numerical simulations illustrate the method’s effectiveness and accuracy.
Journal Article