منابع مشابه
Stochastic Solvers for the Euler Equations
In this paper we extend our previous work, first presented in, to handle effectively non-Gaussian processes and long-time integration in unsteady simulations of compressible flows. Specifically, we apply the generalized polynomial chaos (GPC) method to solve the one-dimensional stochastic Euler equations. We present systematic verification studies against an analytical solution of the stochasti...
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The hydrodynamics of an incompressible fluid can be approximated as a finite dimensional Hamiltonian system by a truncation introduced by Zeitlin [21,22]. With periodic boundary conditions, there exists a family of stationary solutions with vorticity given by Ω∗ = α cos(p · x) + β sin(p · x). Zeitlin’s truncation is used to analyse the linear stability of these solutions and compare this with a...
متن کاملOn a Stochastic Leray-α Model of Euler Equations
We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves conservation of energy. The result holds for initial velocity of finite energy and the solution has finite energy a.s.. These results are easily extended to the 2D ca...
متن کاملNotes on the Euler Equations
These notes describe how to do a piecewise linear or piecewise parabolic method for the Euler equations. 1 Euler equation properties The Euler equations in one dimension appear as: ∂ρ ∂t + ∂(ρu) ∂x = 0 (1) ∂(ρu) ∂t + ∂(ρuu + p) ∂x = 0 (2) ∂(ρE) ∂t + ∂(ρuE + up) ∂x = 0 (3) These represent conservation of mass, momentum, and energy. Here ρ is the density, u is the one-dimensional velocity, p is t...
متن کاملDerandomization of the Euler scheme for scalar stochastic differential equations
Consider a scalar stochastic differential equation with solution process X. We present a deterministic algorithm to approximate the marginal distribution of X at t = 1 by a discrete distribution, and hereby we get a deterministic quadrature rule for expectations E(f(X(1)). The construction of the algorithm is based on a derandomization of the Euler scheme. We provide a worst case analysis for t...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 1999
ISSN: 1050-5164
DOI: 10.1214/aoap/1029962809