Reynolds equation matlab tutorial pdf

It is an example of a simple numerical method for solving the. This is a set of matlab codes to solve the depthaveraged shallow water equations following the method of casulli 1990 in which the freesurface is solved with the theta method and momentum advection is computed with the eulerianlagrangian method elm. Can someone help me simulate the reynolds equation in matlab. However, if you want to suppress and hide the matlab output for an expression, add a semicolon after the expression. Flow instability matlab tutorial bangalore, january 2010. Matlab provides some special expressions for some mathematical symbols, like pi for.

For the sake of easy understanding, take the grid parameter m4, n3 for example to. Flow instability matlab tutorial bangalore, january 2010 matthew juniper, dan henningson, peter schmid 1 1 simple di. The reynolds equation describes pressure variations in thin film flow where the film thickness h is very. Matlab i about the tutorial matlab is a programming language developed by mathworks. As it was already mentioned, the reynolds equation is derived from navierstokes equations. Navierstokes equations with fortran programming language. Thus the time and space discretization, as well as timestepping within the cfl tolerances, are handled directly as a subroutine call to matlab. The pde toolbox is written using matlabs open system philosophy. For example, compressible, nonnewtonian lubricant behavior can be considered. If you complete the whole of this tutorial, you will be able to use matlab to integrate equations of motion for dynamical systems, plot the results, and use matlab optimizers and solvers to make design decisions.

Numerical calculation of oil film for ship stern bearing based on. An example of work that uses advanced computer software is the work of sep, 2006 in which the three. A stable numerical strategy for reynoldsrayleighplesset. Reynolds equation is a partial differential equation of second order. We consider the incompressible navierstokes equations in two space dimensions. A compact and fast matlab code solving the incompressible navierstokes equations on rectangular domains mit18086 navierstokes.

I am a student in master degree and i have a problem as i cannot simulate the reynolds equation in matlab. In the study of fluid lubrication, the core is solving the reynolds equation. No part of this manual may be photocopied or repro duced in any form without. Rating is available when the video has been rented. All models use the transport equation for the turbulent kinetic energy k several transport variables are. Derivation of the solution and the corresponding matlab software. The freesurface equation is computed with the conjugategradient algorithm. By this it is meant that the coe cients of the equation that determines pi. Journal bearing optimization and analysis using streamline. I tried to develop a code in matlab to solve 3 nonlinear equations using newton raphson method, but it seems that the code is not working, does anyone have the ability to fix it. Reynolds equation is the basis for the most practically important applications of hydrodynamic and elastohydrodynamic theories of lubrication. Partial differential equation toolbox users guide math.

Finite element solution of the twodimensional incompressible. These equations describe the flow of a liquid in a rather detailed way. When forming the matrix equation, we need to use a linear indexing to transfer this 2d grid function to a 1d vector function. Mod05 lec23 finite difference method to solve reynolds. A compact and fast matlab code solving the incompressible. Using successive over relaxation sor method in matlab programming obtain the oil film stiffness of the hydraulic confined piston engines hcpe crankshaft. The resulting mathematical equations exhibit the socalled reynolds rayleighplesset rrp coupling.