Method of matched asymptotic expansions

About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.

Difference Methods for Singular Perturbation Problems

Abstract: Preface Part I: Grid Approximations of Singular Perturbation Partial Differential Equations Introduction Boundary Value Problems for Elliptic Reaction-Diffusion Equations in Domains with Smooth Boundaries Boundary Value Problems for Elliptic Reaction-Diffusion Equations in Domains with Piecewise-Smooth Boundaries Generalizations for Elliptic Reaction-Diffusion Equations Parabolic Reaction-Diffusion Equations Elliptic Convection-Diffusion Equations Parabolic Convection-Diffusion Equations Part II: Advanced Trends in epsilon Uniformly Convergent Difference Methods Grid Approximations of Parabolic Reaction-Diffusion Equations with Three Perturbation Parameters Application of Widths for Construction of Difference Schemes for Problems with Moving Boundary Layers High-Order Accurate Numerical Methods for Singularly Perturbed Problems A Finite Difference Scheme on a priori Adapted Grids for a Singularly Perturbed Parabolic Convection-Diffusion Equation On Conditioning of Difference Schemes and Their Matrices for Singularly Perturbed Problems Approximation of Systems of Singularly Perturbed Elliptic Reaction-Diffusion Equations with Two Parameters Survey References

An asymptotic theory of incompressible turbulent boundarylayer flow over a small hump

Abstract: A rational asymptotic theory describing the perturbed flow in a turbulent boundary layer encountering a small two-dimensional hump is presented. The theory is valid in the limit of very high Reynolds number in the case of an aerodynamically smooth surface, or in the limit of small drag coefficient in the case of a rough surface. The method of matched asymptotic expansions is used to obtain a multiple-structured flow, along the general lines of earlier laminar studies. The leading-order velocity perturbations are shown to be precisely the inviscid, irrotational, potential flow solutions over most of the domain. The Reynolds stresses are found to vary across a thin layer adjacent to the surface, and display a singular behaviour near the surface which needs to be resolved by an even thinner wall layer. The Reynolds stress perturbations are calculated by means of a second-order closure model, which is shown to be the minimum level of sophistication capable of describing these variations. The perturbation force on the hump is also calculated, and its order of magnitude is shown to depend on the level of turbulence closure; a cruder turbulence model gives rise to spuriously large forces.

Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation

Abstract: The computational singular perturbation (CSP) method is employed for the solution of stiff PDEs and for the acquisition of the most important physical understanding. The usefulness of the method is demonstrated by analyzing a transient reaction-diffusion problem. It is shown that in the regions where the solution exhibits smooth spatial slopes, a simple nonstiff system of equations can be used instead of the full governing equations. From the simplified system, which is numerically provided by CSP and whose structure varies with space and time, important physical information comes to light. The relation of this method to the class of asymptotic expansion methods is explored. It is shown that the CSP results are identical to the ones obtained by the asymptotic methods. The identifications of the nondimensional parameters and the tedious manipulations needed by the asymptotic methods are performed by programmable numerical or analytic computations specified by CSP. Preliminary numerical results are presented validating the theoretical aspects of the proposed algorithm and providing a measure of its usefulness and its accuracy.