Preconditioners for Linearized Discrete Compressible Euler Equations
نویسنده
چکیده
We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-block-Gauss-Seidel and point-blockILU preconditioners result in iterative solvers with comparable efficiencies.
منابع مشابه
From Discrete Boltzmann Equation to Compressible Linearized Euler Equations
This paper concerns the asymptotic analysis of the linearized Euler limit for a general discrete velocity model of the Boltzmann equation. This is done for any dimension of the physical space, for densities which remain in a suitable small neighbourhood of global Maxwellians. Providing that the initial fluctuations are smooth, the scaled solutions of discrete Boltzmann equation are shown to hav...
متن کاملLINEAR WAVES THAT EXPRESS THE SIMPLEST POSSIBLE PERIODIC STRUCTURE OF THE COMPRESSIBLE EULER EQUATIONS∗ Dedicated to Professor James Glimm on the occasion of his 75th birthday
In this paper we show how the simplest wave structure that balances compression and rarefaction in the nonlinear compressible Euler equations can be represented in a solution of the linearized compressible Euler equations. Such waves are exact solutions of the equations obtained by linearizing the compressible Euler equations about the periodic extension of two constant states separated by entr...
متن کاملThe Importance of Eigenvectors for Local Preconditioners of the Euler Equations
Most previous preconditioning efforts have focused on manipulating the eigenvalues of the spatial operator. For The design of local preconditioners to accelerate the convergence to a steady state for the compressible Euler equations has so far example, Turkel [2] derives a family of preconditioners been solely based on eigenvalue analysis. However, numerical eviwhich reduces the spread of the w...
متن کاملTime-Periodic Linearized Solutions of the Compressible Euler Equations and a Problem of Small Divisors
It has been unknown since the time of Euler whether or not time-periodic sound wave propagation is physically possible in the compressible Euler equations, due mainly to the ubiquitous formation of shock waves. The existence of such waves would confirm the possibility of dissipation free long distance signaling. Following our work in [27], we derive exact linearized solutions that exhibit the s...
متن کاملA Liapunov-schmidt Reduction for Time-periodic Solutions of the Compressible Euler Equations
Following the authors’ earlier work in [9, 10], we show that the nonlinear eigenvalue problem introduced in [10] can be recast in the language of bifurcation theory as a perturbation of a linearized eigenvalue problem. Solutions of this nonlinear eigenvalue problem correspond to time periodic solutions of the compressible Euler equations that exhibit the simplest possible periodic structure ide...
متن کامل