Examples of singular limits in hydrodynamics
نویسنده
چکیده
This chapter is devoted to the study of some asymptotic problems in hydrodynamics. In particular, we will review results about the inviscid limit, the compressible-incompressible limit, the study of rotating fluids at high frequency, the hydrodynamic limit of the Boltzmann equation as well as some homogenization problems in fluid mechanics.
منابع مشابه
Solving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملA simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel
There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...
متن کاملAn effective method for approximating the solution of singular integral equations with Cauchy kernel type
In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...
متن کاملSOLVING SINGULAR ODES IN UNBOUNDED DOMAINS WITH SINC-COLLOCATION METHOD
Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...
متن کاملA General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts
In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...
متن کامل