Three-Dimensional Euler Fluid Code for Fusion Fuel Ignition and Burning
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The document describes a numerical algorithm to simulate plasmas and fluids in the 3 dimensional space by the Euler method, in which the spatial meshes are fixed to the space. The plasmas and fluids move through the spacial Euler mesh boundary. The Euler method can represent a large deformation of the plasmas and fluids. On the other hand, when the plasmas or fluids are compressed to a high density, the spatial resolution should be ensured to describe the density change precisely. The present 3D Euler code is developed to simulate a nuclear fusion fuel ignition and burning. Therefore, the 3D Euler code includes the DT fuel reactions, the alpha particle diffusion, the alpha particle deposition to heat the DT fuel and the DT fuel depletion by the DT reactions, as well as the thermal energy diffusion based on the three-temperature compressible fluid model.Keywords:
Compressible flow
Abstract This paper investigates the benefits of local preconditioning for the compressible Euler equations to predict nearly incompressible fluid flow. The AUSMDV(P) upwind method by Edwards and Liou is employed to maintain the spatial accuracy of the method for low Mach numbers. The results indicate excellent solution quality and fast convergence to steady state for compressible as well as nearly incompressible fluid flow. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Compressible flow
Pressure-correction method
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We consider a $1$-dimensional Lagrangian averaged model for an inviscid compressible fluid. As previously introduced in the literature, such equations are designed to model the effect of fluctuations upon the mean flow in compressible fluids. This paper presents a traveling wave analysis and a numerical study for such a model. The discussion is centered around two issues. One relates to the intriguing wave motions supported by this model. The other is the appropriateness of using Lagrangian-averaged models for compressible flow to approximate shock wave solutions of the compressible Euler equations.
Inviscid flow
Compressible flow
Euler–Lagrange equation
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A simple proof of the Kelvin Theorem, namely conservation of circulation (CC) for solutions of the Euler equation, is given. The result is rewritten in terms of time rescaled variables leading to the Euler-Leray equations, and the implications of CC on the existence of self-similar solutions are discussed.
Circulation (fluid dynamics)
Conservation law
Euler method
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into an infinite target of similar material is also exactly solved by considering a limiting case of this solution. This new compressible flow solution reduces to the classical result of incompressible flow theory when the sound speed of the fluid is allowed to approach infinity. Several illustrations of the differences between compressible and incompressible flows of the type considered are presented.
Compressible flow
Limiting
Incompressible Flow
Infinity
Isothermal flow
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We show that two distinct level sets of the vorticity of a solution to the 2D Euler equations on a disc can approach each other along a curve at an arbitrarily large exponential rate.
Euler method
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Compressible flow
Isentropic process
Fluid parcel
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Compressible flow
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The most common compressible fluids are gases. In fact, all fluids are to some extent compressible but, although liquids vary widely in their compressibility, for many if not quite all purposes they can be treated as incompressible. One situation in which the assumption that liquids are totally incompressible will lead to an erroneous theory is that in which their motions are changed rapidly and in Chapter 8 this circumstance is described.
Compressible flow
Incompressible Flow
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An examination has been made to derive a correlation for an aeroacoustic environment associated with attached compressible flow conditions. It was determined that fluctuating pressure characteristics described by incompressible theory as well as empirical correlations could be modified to a compressible state through a transformation function. In this manner, compressible data were transformed to the incompressible plane where direct use of more tractable prediction techniques are available for engineering design analyses. The investigation centered on algorithms associated with pressure magnitude and power spectral density. The method and subsequent prediction techniques are shown to be in excellent agreement with both incompressible and compressible flow data.
Compressible flow
Incompressible Flow
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This note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations. The obtained solutions vary from a sinusoidal form to a form with singularities. They allow a numerical validation of the free-surface Euler codes.
Free surface
Euler method
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