Three-dimensional Compressible Fluid Research Articles

Deep learning accelerated numerical simulation for three-dimensional compressible fluids

Numerical simulation of fluid flow is a long-standing challenge across many physical application domains, including engineering, climate, and the physical science. There has been a surge of interest in high order schemes aimed at improving simulation accuracy on coarse grids. However, for high-dimensional fluids, the computational cost escalates with the number of dimensions involved. In this paper, we propose a deep learning-based approach to accelerate the numerical computation and further improve the accuracy in simulating three-dimensional (3D) compressible fluids which can be described by Eulerian equations. The proposed work utilizes 3D Euler transformer networks to learn the interpolation coefficients for cell boundaries, which are applied to approximate the boundary fluxes of fluid on coarser grids. Benefiting from learning features of high-resolution fluid flow, our learned interpolation method yields finer performance on coarse grids, thereby accelerating the fluid simulations and improving the numerical accuracy. The numerical experiments confirm that the proposed method improves performance in inference of coarse-grained dynamics.

Local existence and singularities formation for isothermal relativistic radiation hydrodynamics equations

We study the Cauchy problem for multi-dimensional compressible relativistic hydrodynamics in the presence of a radiation field. First, based on the theory of quasilinear symmetric hyperbolic, we establish the local existence of smooth solutions for both non-vacuum and vacuum cases. Next, in the spirit of Sideris’ work [T. Sideris, Formation of singularities of solutions to nonlinear hyperbolic equations, Arch. Ration. Mech. Anal. 86 (1984) 369–381; T. Sideris, Formation of singularities in three-dimensional compressible fluids, Comm. Math. Phys. 101 (1985) 475–485], we show that smooth solutions blow-up in finite time if the initial data is compactly supported and large enough. Compared with the previous work, the main difficulties of the first problem lie in two aspects, we must first deal with the source terms relying on radiative quantities, and we also need to solve out the new coefficients matrices under the Lorentz transformation for vacuum case. The second difficulty arises on how to verifying that the smooth solution has finite propagation speed..

Investigation of acoustic scattering using fast-multipole Padé approximant methods

The scattering of acoustic waves from three-dimensional compressible fluid scatterers is considered. Particular attention is paid to cases where the scatterers have moderate magnitude in compressibility contrast and nondimensional wave number. The scattered field is cast in terms of asymptotic series valid in the limit of small compressibility contrast. It has been shown that pointwise application Pade Approximants in the scattering volume may be used to expand the range of validity of the result. However pointwise divergence in the scattering volume can result as the magnitude of the compressibility contrasted is increased. In this work the utility of low-frequency Fast-multipole method in evaluating the Born series coefficients is examined.

Nonlinear waves in self-gravitating compressible fluid and generalized Cole-Hopf substitutions

A general representation of solutions is constructed for one-dimensional flows of viscous compressible fluid, which allows their exact solutions to be found. A general representation of solutions to Euler equations for three-dimensional compressible fluid flows is found. By analogy, a representation is constructed for flows in a uniformly rotating frame of reference.

Global existence and optimal decay rate of the compressible Navier–Stokes–Korteweg equations with external force

In this paper, we consider the three-dimensional compressible fluid models of Korteweg type. The equation takes the form of the compressible Navier–Stokes equation, with the Cauchy stress tensor in the momentum equations. Under the smallness assumption of the external force in some Sobolev space, we first show the existence of stationary solution by standard iterative arguments. Next, we present that the global-in-time solution of the initial value problem for the three-dimensional compressible Navier–Stokes–Korteweg equations exists uniquely and approaches the stationary solution as t→∞, provided the prescribed initial data and the external force are sufficiently small. Finally, based on the elaborate energy estimates of the solution for the nonlinear system and L2-decay estimates of semigroup generated by the corresponding linearized equation, we show the optimal L2-convergence rates of the solution towards the stationary solution. As far as we know, this is the first result about the global existence and L2-decay rate of smooth solutions for the compressible Navier–Stokes–Korteweg equations with the external force.

Irreducible function bases for simple fluids and liquid crystal films

We present a rigorous derivation of the canonical representation of a class of constitutive functions for liquid crystal films which has been widely used in various special forms in the fields of emulsion chemistry and cell-membrane biology. The representation yields the largest class of functions compatible with an appropriate definition of fluidity. The method used also furnishes established representation formulas in the classical theories of capillarity and three-dimensional compressible fluids.

Parallel finite element algorithm for three-dimensional inviscid and viscous flow

A finite element model is developed and used to simulate three-dimensional compressible fluid flow on a massively parallel computer. The algorithm is based on a Petrov-Galerkin weighting of the convective terms in the governing equations. The discretized time-dependent equations are solved explicitly using a second-order Runge-Kutta scheme. A high degree of parallelism has been achieved utilizing a MasPar MP-2 SIMD computer. An automated conversion program is used to translate the original Fortran 77 code into the Fortran 90 needed for parallelization. This conversion program and the use of compiler directives allows the maintenance of one version of the code for use on either vector or parallel machines. 17 refs.

Vorticity-Velocity Formulation for Three-Dimensional Steady Compressible Flows

The vorticity-velocity formulation of the Navier-Stokes equations is extended to the solution of three-dimensional compressible fluid flow and heat transfer problems. The basic governing equations are expressed in terms of three Poisson-like equations for the velocity components together with a vorticity transport equation and an energy equation. The resulting seven coupled partial differential equations are solved by a finite difference method on a single grid and a discrete solution is obtained by combining a steady-state and a time-dependent Newton's method. Once a converged solution is obtained, one of the velocity equations can be removed from the system and replaced by the continuity equation and a "conservative" solution is obtained by using the previous solution as a starting estimate for Newton's method with only a few additional iterations. The numerical procedure is evaluated by applying it to natural and mixed convection problems. The formulation is found to be stable at high Rayleigh numbers and it may be applied to a wide variety of flow and heat transfer problems.

Formation of singularities in three-dimensional compressible fluids

Presented are several results on the formation of singularities in solutions to the three-dimensional Euler equations for a polytropic, ideal fluid under various assumptions on the initial data. In particular, it is shown that a localized fluid which is initially compressed and outgoing, on average, will develop singularities regardless of the size of the initial disturbance.

A class of three-dimensional compressible fluid flows

A class of three-dimensional compressible fluid flows

On the Asymptotic Behaviour of Three-dimensional Compressible Fluid Flow at a Great Distance from a Body, I. (The Force and Moment on a Solid Body in a Stream of Compressible Fluid)

The steady irrotational isentropic continuous subsonic flow of a perfect gas past an arbitary three-dimensional body with arbitary distribution of sources on its surface is considered. Based on the thing-wingexpansion method, the velocity potential Φ is expanded in the form Φ= U ( x + A 1 r -1 + A 2 r -2 +...), A 1 = a 0 f -1 , A 2 = f -3 [ a 10 cos θ+sin θ( a 11 cos ω+ a 1-1 sin ω)], f =(1- M 2 sin 2 θ) 1/2 , where U is the velocity of the undisturbed flow of Mach number M streaming in the positive direction of x -axis, and x = r cos θ, y = r sin θcos ω, Z = r sin θsin ω. Using this expression, the force ( X , Y , Z ) and moment ( M x , M y , M z ) experienced by the body are found to be: X =ρ ∞ Q ∞ U , Y = Z =0, M x =0, M y , z =± 4π a 1,±1 ρ ∞ U 2 /(1- M 2 ) -1 , where ρ ∞ Q ∞ is the total strength of sources, and ρ ∞ the density at infinity.