Question

Physical significance of laplace equation

Answer 1

In the field of computational analysis, the solution is obtained using iterative schemes, which indirectly solves Naiver stokes equation. Laplace, Poisson, Euler equations are all reduced form of Naiver stokes equation. Thus are significant for Mechanical engineers. For example in the area of computational fluid dynamics, these equations are widely used to obtain better and computationally faster results. You might be familiar about the various initialization schemes available in commercial CFD software, remember a better initialization yields faster results. Standard initialization just inputs the user defined values at all the nodes, this might not be useful every time. There is another kind of initialization called FMG initialization where a coarser grid is considered instead of actual grid and the Euler equation is solved, giving better initial guesses. And in hybrid initialization Laplace equations are solved for still better initial guesses.This is one area where these reduced equations are used. Also analysis these equations and finding a way to solve them, finally gives better insight to solve the much complicated Naiver stokes equation with various boundary conditions for various solution domains .Hope this helps you.Regards.