Solve Navier Stokes Equation with Lax-Wendroff Scheme in Matlab

[omar_mak]

I find a difficulty to generate the code in Matab of Lax-Wendroff scheme to resolve the Navier Stockes equation.

 

[hunt_mat]

What sort of equation are you looking to solve?

 

[omar_mak]

The equations of continuity and Navier Stokes in the case of the coalescence of two bubbles.

 

[hunt_mat]

So are you having problem with generating the finite difference scheme? I did it in my MPhil thesis, take a look if it helps you.

 

[blue_raver22]

The Navier-Stokes equation is a complex partial differential equation that describes the motion of fluids. It is a fundamental equation in fluid dynamics and is used to model a wide range of phenomena, from the flow of air over an airplane wing to the movement of ocean currents.

The Lax-Wendroff scheme is a numerical method used to solve the Navier-Stokes equation. It is a finite difference scheme that approximates the solution to the equation by discretizing the domain and solving for the solution at discrete points in time and space.

To generate the code for the Lax-Wendroff scheme in Matlab, there are a few steps that need to be followed. First, the Navier-Stokes equation needs to be discretized using finite difference methods. This involves approximating the derivatives in the equation using difference equations. Next, the Lax-Wendroff scheme can be implemented by using a forward-time, centered-space approach to solve for the solution at each discrete point in time and space.

There are many resources available online that provide detailed explanations and examples of how to implement the Lax-Wendroff scheme in Matlab for the Navier-Stokes equation. It may be helpful to consult these resources and also reach out to other researchers or colleagues who have experience with numerical methods for fluid dynamics.

It is important to note that solving the Navier-Stokes equation using the Lax-Wendroff scheme in Matlab can be a challenging task, and may require a good understanding of both fluid dynamics and numerical methods. It is also important to carefully validate the results of the code to ensure that they are accurate and reliable.