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Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

P. E. Vincent, A. Jameson (2011)

Mathematical Modelling of Natural Phenomena

Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order...

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Anatoli Babin, Alex Mahalov, Basil Nicolaenko (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear " 2 1 2 dimensional" limit equations...

Feedback stabilization of a boundary layer equation

Jean-Marie Buchot, Jean-Pierre Raymond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...

Feedback stabilization of a boundary layer equation

Jean-Marie Buchot, Jean-Pierre Raymond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2003)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a L Q control problem associated with the linearized equation.

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

Finite differences and boundary element methods for non-stationary viscous incompressible flow

Werner Varnhorn (1994)

Banach Center Publications

We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of...

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