theexactsolution.ItisverifiedthatthelatticeBoltzmannmethodcanachievefirst-order convergence.Therefore,thelatticeBoltzmannmethodisapplicabletofindthesolution fractionalorderNavier-Stokesequation.Themethodiseffective. Keywords:LatticeBoltzmannmethodNumericalmodelingFractionalorder Navier-StokesequationCaputofractionalorderderivative...
摘要Navier-Stokes方程是从复杂的流体运动中简化出来的一个重要模型问题, 通过对这个模型的深入研究,可以帮助我们了解掌握自然规律,从而推动自然 科学的进步。但是Navier-Stokes方程是一个非线性偏微分方程组,求解非常困 难,到目前为止,也只有极少数非常简单的流动问题才能求得其精确解,大多数 还是要通过离散方法求得数...
and α are arbitrary constants, are also solutions of the equation. 2 ◦ . Any solution of the Poisson equation ∆w = C is also a solution of the original equation (these are “inviscid” solutions). 3 ◦ . Solutions in the formof a one-variable function or the sumof functions ...
This equation is often written using the substantive derivative, making it more apparent that this is a statement of Newton's second law: The left side of the equation describes acceleration, and may be composed of time dependent or convective ...
Navier-Stokes equations/ Navier-Stokes equation solutionunstructured triangular mesheslow Mach number modelnumerical methodfinite volume methodunstructured finite elementsfinite difference schemegeneralized coordinate transformationsA low Mach number model of the Navier–Stokes equations has been developed for ...
In Chaps. 3, 4 and 6 we dealt with the discretization of a generic conservation equation. The discretization principles described there apply to the momentum and continuity equations (which we shall collectively call the Navier-Stokes equations) . In thi
dividing the equation by ρ. Note that in the incompressible case (17.2) the energy equation has disappeared. Indeed, even though such an equation can still be written for incompressible flows, its solution can be found independently once the velocity field is obtained from the solution of (...
L. Ross , “ Numerical Solution of the Navier-Stokes Equation for Flow Past Spheres: Part I. Viscous Flow around Spheres with and without Radial Mass Efflux ,” AIChE J. , 13 , 212 ( 1967 ).Hamielec, A. E., Hoffman, T. W., and Ross, L. L., "Numerical Solution of the Navier...
Thus the governing equation is an integro-differential equation and not convenient for numerical computation. An equivalent weak or variational form of the equation, proved to produce the same velocity solution as the Navier–Stokes equation,[18] is given by, for divergence-free test functions ...
is the self-similar solution with initial data U 0 (x) and r(x, t) ∈ L ∞ ([0, T) × 3 ). (17) Proofs. We first reformulate the problem in order to obtain an integral equation for u. This is standard practice, and was first employed by Kato and Fujita (see [8][9]...