An Example of Self–Acceleration for Incompressible Flows
نویسندگان
چکیده
Here ν = 0 for the Euler equation and ν > 0 for the Navier–Stokes equation. We assume that the initial vector field, v(x, 0) = u(x), is given by a smooth, bounded, divergence–free function u(x) of finite energy. Then a smooth solution v(x, t) is known to exist in some finite time interval 0 ≤ t < T . It is an open problem, for both the Euler and the Navier–Stokes equations, if blow–up can occur in finite time or if a smooth solution v(x, t) always exists for 0 ≤ t <∞.
منابع مشابه
External and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملThree-dimensional characteristic approach for incompressible thermo-flows and influence of artificial compressibility parameter
In this paper the characteristics of unsteady three-dimensional incompressible flows with heat transfer are obtained along with artificial compressibility of Chorin. At first, compatibility equations and pseudo characteristics for three-dimensional flows are derived from five governing equations (continuity equation, Momentum equations in three directions, and energy equation) and then results ...
متن کاملSimulation of Gravity Wave Propagation in Free Surface Flows by an Incompressible SPH Algorithm
This paper presents an incompressible smoothed particle hydrodynamics (SPH) model to simulate wave propagation in a free surface flow. The Navier-Stokes equations are solved in a Lagrangian framework using a three-step fractional method. In the first step, a temporary velocity field is provided according to the relevant body forces. This velocity field is renewed in the second step to include t...
متن کاملDevelopment of an explicit pressure-based unstructured solver for three-dimensional incompressible flows with graphics hardware acceleration
متن کامل
Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes
In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynam...
متن کامل