Equations Of Gas Dynamics Research Articles

Numerical Study of Complex Heat Transfer and Aerodynamics in a Tube Furnace with a Flat Fuel Combustion Mode

The object of the study is a tubular furnace for steam reforming of natural gas. The channel walls are formed by a refractory lining and a tubular screen with a known temperature. The chamber volume is filled with a selectively radiating, absorbing and weakly scattering medium of gaseous fuel combustion products. The research method is based on the numerical solution of a system of two-dimensional integro-differential equations of radiative gas dynamics, closed by a two-parameter model of turbulent convection. It is shown that when burners are located on the side walls of the radiation chamber, a significant restructuring of the heat flux distribution occurs. A decrease in the chamber width is accompanied by an increase in both radiant and convective heat fluxes to the tubular screen.

A Novel Approach for Time-Local Fractional Solutions of Certain Nonlinear Partial Differential Equations in Fractal Dimension

Time-local fractional approaches for nonlinear partial differential equations in fractal dimensions are essential for capturing the complex, irregular behaviors found in fractal systems. In this paper, a new modification of the local fractional Laplace variational iteration method (MLFLVIM) for obtaining analytical approximate solutions to the fractional gas dynamics equation, fractional Stefan equation, and fractional Newell-Whitehead-Segel equation within the context of fractal time space is presented. The proposed method (MLFLVIM) elegantly combines the local fractional Laplace transform (LFLT) with modified variational iteration method. Specifically, we first apply the (LFLT) to the given local fractional PDEs, yielding a transformed system of equations. We then apply modified variational iteration to this system. Finally, we use the inverse of (LFLT) to obtain the desired solution. To demonstrate the effectiveness of this approach, we implement it on three numerical physical problems. The results show that the (MLFLVIM) can successfully handle these nonlinear LFPDEs and provide accurate analytical approximation solutions.

On Godunov's interesting class of systems - The symmetric hyperbolic Euler equations of gas dynamics

On Godunov's interesting class of systems - The symmetric hyperbolic Euler equations of gas dynamics

Memoirs of finite difference schemes

The report contains recollections of the invention of one of the methods for solving gas dynamics equations (1953 - 1969). Serious attention is given to questions for which answers are still unknown to this day. This report is intended for researchers, engineers, and those interested in the history of mathematics.

An induced limitation in the reconstruction step for Euler equations of compressible gas dynamics in arbitrary dimension

An induced limitation in the reconstruction step for Euler equations of compressible gas dynamics in arbitrary dimension

Approximate and Exact Solutions of Some Nonlinear Differential Equations Using the Novel Coupling Approach in the Sense of Conformable Fractional Derivative

Several scientific fields utilize fractional nonlinear partial differential equations to model various phenomena. However, most of these equations lack exact solutions. Consequently, techniques for obtaining approximate solutions, which sometimes yield exact solutions, are essential. In this research, we develop a new approach by combining the homotopy perturbation method (HPM) and the conformable natural transform to solve the gas-dynamic equation (GDE), the Fokker-Planck equation (FPE), and the Swift-Hohenberg equation (SHE) in the context of conformable derivatives. The proposed approach is called the conformable natural homotopy perturbation method (CNHPM). This approach has the advantage of not requiring assumptions about significant or minor physical factors. Consequently, it eliminates some of the constraints associated with conventional perturbation methods and can solve both weak and highly nonlinear problems. We consider the absolute, relative, and residual errors numerically and graphically to assess the correctness of our approach. The results show that our approach serves as a suitable alternative to the approximate methods in the literature for solving fractional differential equations.

On the Energy Cost for Nitrogen Fixation in DC Glow Discharges in Atmospheric‐Pressure Air

ABSTRACTModeling of the production of nitrogen oxide molecules in DC discharges in laminar longitudinal flows of atmospheric‐pressure air is performed. Two‐dimensional nonequilibrium discharge model includes the system of gas dynamic equations and balance equations for various plasma components. Simulations are performed for the discharge currents 50–600 mA and gas flow velocities 1–10 m/s. In considered conditions, the gas temperature in the discharge core varies in the range of 3000–6000 K. Spatial profiles of the densities and fluxes of produced species are obtained, both inside the discharge and in the afterglow region. The energy cost for the production of nitrogen oxides is calculated, depending on the discharge current, gap length, and gas flow velocity. The results of the simulation are compared with available experimental data.

An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier–Stokes equations

We consider an optimization-based limiter for enforcing positivity of internal energy in a semi-implicit scheme for solving gas dynamics equations. With Strang splitting, the compressible Navier–Stokes system is split into the compressible Euler equations, which are solved by the positivity-preserving Runge–Kutta discontinuous Galerkin (DG) method, and the parabolic subproblem, which is solved by Crank–Nicolson in time with interior penalty DG method. Such a scheme is at most second order accurate in time, high order accurate in space, conservative, and preserves positivity of density. To further enforce the positivity of internal energy, we impose an optimization-based limiter for the total energy variable to post-process DG polynomial cell averages. The optimization-based limiter can be efficiently implemented by the popular first order convex optimization algorithms such as the Douglas–Rachford splitting method by using nearly optimal algorithm parameters. Numerical tests suggest that the DG method with Qk basis and the optimization-based limiter is robust for demanding low-pressure problems such as high-speed flows.

Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation

We applied a method of symmetry reduction to the gas dynamics equations with a special form of the equation of state. This equation of state is a pressure represented as the sum of a density and an entropy functions. The symmetry Lie algebra of the system is 12-dimensional. One, two and three-dimensional subalgebras were considered. In this article, four-dimensional subalgebras are considered for the first time. Specifically, invariants are calculated for 50 four-dimensional subalgebras. Using invariants of one of the subalgebras, a symmetry reduction of the original system is calculated. The reduced system is a partially invariant submodel because one gas-dynamic function cannot be expressed in terms of the invariants. The submodel leads to two families of exact solutions, one of which describes the isochoric motion of the media, and the other solution specifies an arbitrary blow-up surface. For the first family of solutions, the particle trajectories are parabolas or rays; for the second family of solutions, the particles move along cubic parabolas or straight lines. From each point of the blow-up surface, particles fly out at different speeds and end up on a straight line at any other fixed moment in time. A description of the motion of particles for each family of solutions is given.

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024) [12], a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

Dynamics of a Discharge Initiated by a Powerful Femtosecond Laser Pulse in Atmospheric Pressure Air in Pre-Breakdown Electrical Fields

Numerical modeling of the dynamics of a discharge initiated by a high-power femtosecond laser pulse in air at atmospheric pressure in pre-breakdown fields was carried out. Calculations were conducted within the framework of a 1D-axisymmetric model that describes the evolution of the radial profiles of the main parameters of the discharge under study. The model includes a system of reaction that determine gas heating and a detailed description of the kinetic processes in a given discharge, as well as a system of gas-dynamic equations to describe the expansions of the heated channel. The results of calculations of the breakdown time of the discharge gap are conсistent with the measurement data over the entire studied range of electric field strengths, E = 9–17 kV/cm. It is shown that one of the key factors determining the evolution of the parameters of a given discharge is the rate of gas heating.

An Approach to Solve Gas Dynamic Equation by Fuzzy Hilfer Fractional Differential Equation

In this work, Adomian decomposition method (ADM) based on Hilfer derivative is proposed to solve nonlinear fuzzy fractional gas dynamic equation. We reform the provided fractional gas dynamic equation into fuzzy Hilfer fractional differential equation. Subsequently with description of Hilfer fractional derivative and suitable initial conditions under fuzzy sense, we obtain approximate solution to the given problem. This method provides an analytical solution in the form of infinite power series. The behavior of the solution is illustrated using graphical representation.

Analysis of different modiҥcations of the CABARET scheme applied for approximation of the system of gas-dynamic equations

Analysis of different modiҥcations of the CABARET scheme applied for approximation of the system of gas-dynamic equations

Ten-moment fluid model with heat flux closure for gasdynamic flows

The gasdynamic 10-moment equations are revisited, applying a Chapman-Enskog type expansion to achieve the closure for heat flux. The resulting gradient-based closure performs favorably against previously employed closures in regions of shocks when compared to the kinetic results obtained from Direct Simulation Monte Carlo simulations. The 10-moment model can capture finite kinetic effects due to non-Maxwellian velocity distribution functions, as compared to the 5-moment Navier-Stokes equations, and remains hyperbolic-parabolic with real wave speeds under all initial conditions. Self-consistent kinetic boundary conditions are derived without consideration of a distinct Knudsen layer. The model is applied to a number of canonical gasdynamics problems in one and two dimensions such as steady normal and oblique shocks, as well as the Sod shock tube problem.

Classical and Quantum Mechanical Models of Many-Particle Systems

The workshop focused on the collective behavior of many-particle systems in various application fields: physics (gas dynamics, plasmas, quantum mechanics), mathematical biology (cell mobility, evolution of trait-structured species), and social sciences (wealth distribution). This includes famous models such as the Boltzmann equation of gas dynamics, Vlasov equation for plasmas, Fokker–Planck equations, Smoluchowski and related equations, Keller–Segel system of chemotaxis.

Symmetry Analysis of the Two-Dimensional Stationary Gas Dynamics Equations in Lagrangian Coordinates

This article analyzes the symmetry of two-dimensional stationary gas dynamics equations in Lagrangian coordinates, including the search for equivalence transformations, the group classification of equations, the derivation of group foliations, and the construction of conservation laws. The consideration of equations in Lagrangian coordinates significantly simplifies the procedure for obtaining conservation laws, which are derived using the Noether theorem. The final part of the work is devoted to group foliations of the gas dynamics equations, including for the nonstationary isentropic case. The group foliations approach is usually employed for equations that admit infinite-dimensional groups of transformations (which is exactly the case for the gas dynamics equations in Lagrangian coordinates) and may make it possible to simplify their further analysis. The results obtained in this regard generalize previously known results for the two-dimensional shallow water equations in Lagrangian coordinates.

Cell-centered indirect Arbitrary Lagrangian-Eulerian numerical strategy for solving 3D gas dynamics equations

Solving the Euler equations under the Lagrangian formalism enables to simulate various complex engineering applications. However, the use of this formalism can lead to significant mesh deformations as the mesh follows the fluid velocity. The mesh quality may be considerably deteriorated requiring a regularization procedure. In the present document, it is shown that the ideas presented by J. Yao (2013)[68] and J. Yao and D. Stillman (2016) [30] may be used efficiently in a 3D hydrodynamics code to perform reliable regularization steps. The flexibility of the methodology in addition to its simplicity, since it only relies on trivial geometrical considerations, opens the way for various extensions. The remapping step then considered, uses the geometrical splitting procedure of the Lagrangian phase to perform effective projections. This coherence ensures the compactness of the overall algorithm. At last but not least, a 3D Flux-Corrected-Remapping method is presented. This yields a particularly robust remapping algorithm while also leading the way for higher order projection extensions.

Deep smoothness weighted essentially non-oscillatory method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators

In this work, we enhance the fifth-order Weighted Essentially Non-Oscillatory (WENO) shock-capturing scheme by integrating deep learning techniques. We improve the established WENO algorithm by training a compact neural network to dynamically adjust the smoothness indicators within the WENO scheme. This modification boosts the accuracy of the numerical results, particularly in proximity to abrupt shocks. Notably, our approach eliminates the need for additional post-processing steps, distinguishing it from previous deep learning-based methods. We substantiate the superiority of our new approach through the examination of multiple examples from the literature concerning the two-dimensional Euler equations of gas dynamics. Through a thorough investigation of these test problems, encompassing various shocks and rarefaction waves, our novel technique consistently outperforms the traditional fifth-order WENO scheme. This superiority is especially evident in cases where numerical solutions exhibit excessive diffusion or overshoot around shocks.

Interactions between elementary waves and weak discontinuity in two-layer blood flow through artery

Blood flow through arterial circulation can be characterized by fluid transport in flexible tubes and modeled mathematically using the conservation of mass and momentum. A one-dimensional model for two-layer blood flow with different blood velocities and the same constant density in each layer derived from the Euler equations of gas dynamics by taking the vertical average across each layer. This work presents interactions of elementary waves with a weak discontinuity for the quasilinear 3 × 3 system of conservation laws governing the two-layer blood flow in arteries. Exploiting elementary waves as a single-parameter curve, we study the Riemann solution uniquely and consequently establish the condition on initial data for the existence of a solution to the Riemann problem. Furthermore, we discuss the evolution of weak discontinuity waves and subsequently derive their amplitudes; in what follows, we investigate the interactions of weak discontinuity with contact discontinuity and shocks. Finally, a series of numerical tests have been performed to understand the impact of shock strength and the initial data on the amplitudes of reflected and transmitted waves and the jumps in shock acceleration.

Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics

Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics