Search results for "euler equation"
showing 10 items of 36 documents
Zero Viscosity Limit for Analytic Solutions of the Primitive Equations
2016
The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\). The main assumption is spatial analyticity of the initial datum.
Adaptive discontinuous evolution Galerkin method for dry atmospheric flow
2014
We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realiz…
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Properties of condensed spin-aligned atomic hydrogen from variational calculations
1979
The optimal Jastrow-type ground-state wave function of spin-aligned atomic hydrogen is calculated using the pair potential of Kolos and Wolniewicz. The optimization is performed by solving the Euler equation in the hypernetted chain approximation. Accurate energies as well as pair-distribution functions are obtained. The Bose-Einstein condensate fraction is evaluated from the one-particle momentum distribution. The pair distribution function is also used to obtain stability criteria for the system and minimal values for the aligning magnetic field are calculated at low densities. The resulting values of the minimal aligning fields are considerably higher than those obtained previously.
Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function
2021
We give an overview on the work developed in recent years about certain classes of incomplete Riemann solvers for hyperbolic systems. These solvers are based on polynomial or rational approximations to |x|, and they do not require the knowledge of the complete eigenstructure of the system, but only a bound on the maximum wave speed. Our solvers can be readily applied to nonconservative hyperbolic systems, by following the theory of path-conservative schemes. In particular, this allows for an automatic treatment of source or coupling terms in systems of balance laws. The properties of our schemes have been tested with some challenging numerical experiments involving systems such as the Euler…
Un modelo no hidrostático global con coordenada vertical basada en altura
2015
Memoria presentada en la Universitat de València para optar grado de de Doctor Esta tesis documenta la investigación que he realizado en modelización atmosférica: se parte de las ecuaciones físicas de la atmósfera y se aplican métodos numéricos eficientes para encontrar una solución a dichas ecuaciones a partir de unas condiciones iniciales dadas. Para este fin, se ha desarrollado un modelo atmosférico cuyas características principales son: espectral en la representación horizontal de los campos, discretización vertical de alto orden de exactitud, y semi-implícito en la integración temporal. Además, el modelo es no hidrostático y tiene una coordenada vertical basada en altura, en vez de la …
On new ways of group methods for reduction of evolution-type equations
2005
AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.
Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations
1998
This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.
Navier-Stokes equations on an exterior circular domain: construction of the solution and the zero viscosity limit
1997
Abstract In this Note, we consider the limit of Navier-Stokes equations on a circular domain. By an explicit construction of the solution, it is proved that, when viscosity goes to zero, solution converges to the Euler solution outside the boundary layer and to the Prandtl solution inside the boundary layer.
Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms
1999
SUMMARY A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensi…