Search results for "Explicit solution"
showing 4 items of 4 documents
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
2011
Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.
Explicit Bézier control net of a PDE surface
2017
The PDE under study here is a general fourth-order linear elliptic Partial Differential Equation. Having prescribed the boundary control points, we provide the explicit expression of the whole control net of the associated PDE Bézier surface. In other words, we obtain the explicit expressions of the interior control points as linear combinations of free boundary control points. The set of scalar coefficients of these combinations works like a mould for PDE surfaces. Thus, once this mould has been computed for a given degree, real-time manipulation of the resulting surfaces becomes possible by modifying the prescribed information. The work was partially supported by Spanish Ministry of Econo…
Generating harmonic surfaces for interactive design
2014
Abstract A method is given for generating harmonic tensor product Bezier surfaces and the explicit expression of each point in the control net is provided as a linear combination of prescribed boundary control points. The matrix of scalar coefficients of these combinations works like a mould for harmonic surfaces. Thus, real-time manipulation of the resulting surfaces subject to modification of prescribed information is possible.