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result(s) for
"Gas dynamics."
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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
New Low-Dissipation Central-Upwind Schemes
In this paper, we develop new second-order low-dissipation central-upwind (LDCU) schemes for hyperbolic systems of conservation laws. Like all of the Godunov-type schemes, the proposed LDCU schemes are developed in three steps: reconstruction, evolution, and projection. A major novelty of our approach is in the projection step, which is based on a subcell resolution and designed to sharper approximate contact waves while ensuring a non-oscillatory property of the projected solution. In order to achieve this goal, we take into account properties of the contact waves. We design the LDCU schemes for both the one- and two-dimensional Euler equations of gas dynamics. The new schemes are tested on a variety of numerical examples. The obtained results clearly demonstrate that the proposed LDCU schemes contain substantially smaller amount of numerical dissipation and achieve higher resolution compared with their existing counterparts.
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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
Effect of Different Surface Microstructures in the Thermally Induced Self-Propulsion Phenomenon
In micro/nano-scale systems where the characteristic length is in the order of or less than the mean free path for gas molecules, an object placed close to a heated substrate with a surface microstructure receives a propulsive force. In addition to the induced forces on the boundaries, thermally driven flows can also be induced in such conditions. As the force exerted on the object is caused by momentum brought by gas molecules impinging on and reflected at the surface of the object, reproducing molecular gas flows around the object is required to investigate the force on it. Using the direct simulation Monte Carlo (DSMC) method to resolve the flow, we found that by modifying the conventional ratchet-shaped microstructure into different configurations, a stronger propulsive force can be achieved. Specifically, the tip angle of the microstructure is an important parameter in optimizing the induced force. The increase in the propulsive force induced by the different microstructures was also found to depend on the Knudsen number, i.e., the ratio of the mean free path to the characteristic length and the temperature difference between the heated microstructure and the colder object. Furthermore, we explained how this force is formed and why this force is enhanced by the decreasing tip angle, considering the momentum brought onto the bottom surface of the object by incident molecules.
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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
On the high friction limit for the complete Euler system
We show that solutions of the complete Euler system of gas dynamics perturbed by a friction term converge to a solution of the porous medium equation in the high friction/long time limit. The result holds in the largest possible class of generalized solutions–the measure–valued solutions of the Euler system.
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
Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method
In this article, the ( G ′ / G ) -expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie’s operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in ( G ′ / G ) , where G = G ( ξ ) satisfies a second order linear ordinary differential equation. In this paper, ( G ′ / G ) -expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions.
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. nema
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