arildno said:I found this book good:
Bender&Orszag
``Advanced Mathematical methods for scientists and engineers''
Here's an amazon link:
https://www.amazon.com/gp/product/0070661731/?tag=pfamazon01-20
arildno said:Well, have you looked after articles about multiple boundary layer theory?
From what I know, it has become rather common to develop a tripartite boundary layer with various powers of the Reynolds number as the distinguishing marks between the layers.
Evidently, asymptotic matching will be needed to weld together the local solutions.
Asymptotic matching is a mathematical technique used to simplify complex fluid mechanics problems by breaking them down into simpler, asymptotically equivalent problems. This allows for a more efficient and accurate solution to be found.
Asymptotic matching is used to match the solutions of two different fluid mechanics problems at a common boundary, typically at the interface between two fluids. This allows for the boundary conditions of one problem to be used in the other, simplifying the overall solution.
The main benefit of using asymptotic matching is that it allows for the simplification of complex fluid mechanics problems, making them easier to solve and providing more accurate results. It also reduces the amount of computation required, making the solution process more efficient.
Asymptotic matching is commonly used in various areas of fluid mechanics, such as in the study of boundary layers, shock waves, and waves in stratified fluids. It is also used in the analysis of flow in porous media and in problems involving multiple fluids.
While asymptotic matching is a powerful tool in fluid mechanics, it does have its limitations. It is most effective for problems with well-defined boundary conditions and when the solutions can be approximated by a series expansion. It may also fail in cases where the boundary conditions are not smooth or when there are significant nonlinearities in the problem.