scholarly journals Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver

1994 ◽  
Author(s):  
Kumud Ajmani ◽  
Arthur Taylor, III
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sensitivity Derivatives ◽  
Discrete Sensitivity ◽  
Derivatives Of

Navier Stokes Derivative Estimates in Three Dimensions with Boundary Values and Body Forces

1991 ◽  
Vol 43 (6) ◽  
pp. 1161-1212 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Stokes Equations ◽  
Finite Energy ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Boundary Values ◽  
Vector Solution ◽  
Navier Stokes Equations ◽  
Body Forces ◽  
Derivatives Of

AbstractFor a vector solution u(x, t) with finite energy of the Navier Stokes equations with body forces and boundary values on a region Ω ⊆ R3 for t > 0, conditions are established on the L6/5(Ω) and L2(Ω) norms of derivatives of the data that ensure the estimates and max , up to any given integer value of the weighted order 2r+s, where r or s = s1 + s2 + s3 > 0 and 0 < T < ∞.

Parametric Study of a Turbine Blade Cascade Using a New Parametric Flow Solver Turb’Opty

2002 ◽  
Author(s):  
S. Moreau ◽  
S. Aubert ◽  
M. N’Diaye ◽  
P. Ferrand ◽  
J. Tournier ◽  
...  
Keyword(s):  
Turbine Blade ◽  
Stokes Equations ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Reference Solution ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Blade Cascade ◽  
Polynomial Reconstruction ◽  
Derivatives Of

A new parameterized CFD solver Turb’Opty™ has been developed based on a Taylor series expansion to high order derivatives of the solutions of the discretized Navier-Stokes equations. The method has been successfully applied to the laminar compressible flow field of the T106 turbine blade cascade. Comparisons with the classical CFD results have validated the accuracy of the parameterized solutions obtained by a simple polynomial reconstruction around a reference solution. The CPU efficiency has been emphasized by quickly computing the performance maps (power and losses) of this blade cascade. Wide industrial perspectives of turbomachinery global optimization are finally demonstrated by coupling this method with a simple genetic algorithm.

Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces

2018 ◽  
Vol 18 (3) ◽  
pp. 517-535 ◽  
Author(s):  
Minghua Yang ◽  
Zunwei Fu ◽  
Suying Liu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Gevrey Regularity ◽  
Navier Stokes Equations ◽  
Global Existence Of Solutions ◽  
Regularity Estimates ◽  
Gevrey Estimates ◽  
The Cauchy Problem ◽  
Critical Besov Spaces ◽  
Derivatives Of

Abstract This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the solutions are analytic for a small interval of time with values in a Gevrey class of functions. As a consequence of Gevrey estimates, we particularly imply higher-order derivatives of solutions in Besov and Lebesgue spaces. Moreover, we prove that the existence of a positive constant {\tilde{C}} such that the initial data {(u_{0},n_{0},c_{0}):=(u_{0}^{h},u_{0}^{3},n_{0},c_{0})} satisfy \tilde{C}\bigl{(}\lVert(n_{0},c_{0})\rVert_{\dot{B}^{-2+3/q}_{q,1}(\mathbb{R}^% {3})\times\dot{B}^{3/q}_{q,1}(\mathbb{R}^{3})}+\lVert u_{0}^{h}\rVert_{\dot{B}% ^{-1+3/p}_{p,1}(\mathbb{R}^{3})}+\lVert u_{0}^{h}\rVert_{\dot{B}^{-1+3/p}_{p,1% }(\mathbb{R}^{3})}^{\alpha}\lVert u_{0}^{3}\rVert_{\dot{B}^{-1+3/p}_{p,1}(% \mathbb{R}^{3})}^{1-\alpha}\bigr{)}\leq 1 for certain conditions on {p,q} and α implies the global existence of solutions with large initial vertical velocity component.

THE KOLMOGOROV EQUATION ASSOCIATED TO THE STOCHASTIC NAVIER–STOKES EQUATIONS IN 2D

2004 ◽  
Vol 07 (02) ◽  
pp. 163-182 ◽  
Author(s):  
VIOREL BARBU ◽  
GIUSEPPE DA PRATO ◽  
ARNAUD DEBUSSCHE
Keyword(s):  
Invariant Measure ◽  
Stokes Equations ◽  
Dirichlet Boundary Conditions ◽  
Kolmogorov Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Sharp Estimates ◽  
Stochastic Term ◽  
Derivatives Of

We consider a 2D Navier–Stokes equation with Dirichlet boundary conditions perturbed by a stochastic term of the form [Formula: see text], where Q is a non-negative operator and Ẇ is a spacetime white noise. We solve the corresponding Kolmogorov equation in the space L2(H,ν) where ν is an invariant measure and prove the "carré du champs" identity. The key tool are some sharp estimates on the derivatives of the solution. Our main assumption is that the viscosity is large compared with the norm of Q. As a byproduct, we give a new simple proof of the uniqueness of the invariant measure and obtain an existence result for a Hamilton–Jacobi equation related to a control problem.

scholarly journals Turbine cascade design via multigrid-aided finite-difference progressive optimization

2008 ◽  
pp. 199-215
Author(s):  
Luciano A. Catalano ◽  
Andrea Dadone ◽  
Vito S.E. Daloiso
Keyword(s):  
Design Optimization ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Computational Time ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Fine Mesh ◽  
Sensitivity Derivatives ◽  
Volume Method

This paper proposes an efficient and robust procedure for the design optimization of turbomachinery cascades in inviscid and turbulent transonic flow conditions. It employs a progressive strategy, based on the simultaneous convergence of the design process and of all iterative solutions involved (flow analysis, gradient evaluation), also including the global refinement from a coarse to a sufficiently fine mesh. Cheap, flexible and easy-to-program Multigrid-Aided Finite Differences are employed for the computation of the sensitivity derivatives. The entire approach is combined with an upwind finite-volume method for the Euler and the Navier-Stokes equations on cell-vertex unstructured (triangular) grids, and validated versus the inverse design of a turbine cascade. The methodology turns out to be robust and highly efficient, the converged design optimization being obtained in a computational time equal to that required by 15 to 20 (depending on the application) multigrid flow analyses on the finest grid.

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