Search results for "euler equation"
showing 10 items of 36 documents
The Numerical Simulation of Relativistic Fluid Flow with Strong Shocks
2001
In this review we present and analyze the performance of a Go-dunov type method applied to relativistic fluid flow. Our model equations are the corresponding Euler equations for special relativistic hydrodynamics. By choosing an appropriate vector of unknowns, the equations of special relativistic fluid dynamics (RFD) can be written as a hyperbolic system of conservation laws. We give a complete description of the spectral decomposition of the Jacobian matrices associated to the fluxes in each spatial direction, (see (Donat et al., 1998), for details), which is the essential ingredient of the Godunov-type numerical method we propose in this paper. We also review a numerical flux formula tha…
A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows
2013
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
2016
We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space $$L_t^\infty L_x^2$$ , satisfying appropriate vorticity estimates. We also obtain impr…
Equilibrium real gas computations using Marquina's scheme
2003
Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness
An order-adaptive compact approximation Taylor method for systems of conservation laws
2021
Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…
Dense solid–liquid off-bottom suspension dynamics: Simulation and experiment
2009
Dense solid–liquid off-bottom suspension inside a baffled mechanically stirred tank equipped with a standard Rushton turbine is investigated. Dynamic evolution of the suspension from start-up to steady-state conditions has been determined by both visual experiments and computational fluid dynamics (CFDs). A classical Eulerian–Eulerian multifluid model (MFM) along with the “homogeneous” k–ε turbulence model is adopted to simulate suspension dynamics. In these systems the drag inter-phase force affects both solids suspension and distribution. Therefore, different computational approaches are tested in order to compute this term. Simulation results are compared with images obtained from the re…
CFD Simulation of Particle Suspension Height in Stirred Vessels
2004
Computational fluid dynamics (CFD) simulation capabilities for stirred solid–liquid dense systems are explored. These systems may give rise to the formation of a thick and well defined clear liquid layer in the upper part of the vessel, whose extension progressively reduces with increasing impeller speed. Experimental measurements of the suspension height (the height of the particle laden layer) were carried out at various agitation speeds for a variety of solid–liquid systems in a fully baffled transparent tank. A clear layer of liquid was actually observed in all runs, with the suspension height almost linearly dependent on agitation speed. CFD simulations of the above described systems w…
Capturing blast waves in granular flow
2007
Abstract In this paper we continue the analysis of compressible Euler equations for inelastic granular gases described by a granular equation of state due to Goldshtein and Shapiro [Goldshtein A, Shapiro M. Mechanics of collisional motion of granular materials. Part 1: General hydrodynamic equations. J Fluid Mech 1995;282:75–114], and an energy loss term accounting for inelastic collisions. We study the hydrodynamics of blast waves in granular gases by means of a fifth-order accurate scheme that resolves the evolution under different restitution coefficients. We have observed and analyzed the formation of a cluster region near the contact wave using the one-dimensional and two-dimensional v…
Capturing shock waves in inelastic granular gases
2005
Shock waves in granular gases generated by hitting an obstacle at rest are treated by means of a shock capturing scheme that approximates the Euler equations of granular gas dynamics with an equation of state (EOS), introduced by Goldshtein and Shapiro [J. Fluid Mech. 282 (1995) 75-114], that takes into account the inelastic collisions of granules. We include a sink term in the energy balance to account for dissipation of the granular motion by collisional inelasticity, proposed by Haff [J. Fluid Mech. 134 (1983) 401-430], and the gravity field added as source terms. We have computed the approximate solution to a one-dimensional granular gas falling on a plate under the acceleration of grav…
A flux-split algorithm applied to conservative models for multicomponent compressible flows
2003
In this paper we consider a conservative extension of the Euler equations for gas dynamics to describe a two-component compressible flow in Cartesian coordinates. It is well known that classical shock-capturing schemes applied to conservative models are oscillatory near the interface between the two gases. Several authors have addressed this problem proposing either a primitive consistent algorithm [J. Comput. Phys. 112 (1994) 31] or Lagrangian ingredients (Ghost Fluid Method by Fedkiw et al. [J. Comput. Phys. 152 (1999) 452] and [J. Comput. Phys. 169 (2001) 594]). We solve directly this conservative model by a flux-split algorithm, due to the first author (see [J. Comput. Phys. 125 (1996) …