Evaluating the results of a Lax-Wendroff scheme on 1-D flux

[SimoneC618]

Homework Statement

Analyze the flux properties in an ICE manifold using 1D numerical methods such as Lax-Wendroff or Lax-Friederichs

Relevant Equations

initial conditions: P_0 = 101325 Pa; T_0 = 293,15 K.

Hi everyone,
i'm very new to the forum so i hope I've used the correct form to write my question.

Anyway, i need some help to evaluate the result of my last analysis: I'm studying the flux flowing inside an ICE aspiration manifold in a very simplified way (1D flux, ideal gas, compressible flow). For the analysis I've implemented the Matlab code for a Lax-Wendroff scheme and for a Lax-Friderichs scheme using the following assumptions:

the air aspirated in the manifold is initially in the ambient condition;

the conditions at the inlet could be find using the energy and mass conservation law that give: T1 = 293.08 K ; P1 = 95421.5 Pa ; u1 = 2.77 m/s.

the pressure value at the outlet can be found assuming the rotation speed of the engine (n = 6000 rpm) and knowing the geometry of the cylinder;
the value I've found is about 5kPa, so P2 = 90161 Pa

Now, i have to solve the mass, momentum and energy conservation in the conservative form with numerical schemes I've mentioned above.
To avoid writing a very long message i attach my code and i hope you can understand all the steps.

Now the question: do you think the plots i obtained are correct? Is that what you expect from a Lax-Wendroff scheme?
To be onest i think something in my Lax Wendroff scheme is not working because the plots I've obtained show the solution is not converging and that would mean the scheme is not stable, but it should be more stable than Lax-Friederichs one! Moreover, i expect my solution to converge or, at least, to stabilize in a little range of values.

Well, I'm sorry for my bad grammar and i hope you can help me.
Best regards.

 

[bigfooted]

Hi! Well, have you tested your code with the standard equation du/dt + a*du/dx = 0 ? This is probably the case that was discussed with example solutions in a lecture belonging to this course.
You can then check if the numerical method was implemented correctly. You can then extend your verified code by making it accept a vector U instead of a scalar u. The first verification is then that your code still produces the same correct results if the vector U=. You can then extend the code to accept the variables that are necessary for your code. You can also introduce variables like u1=rho, u2=rho*U,... if needed to keep the shape of the equation as d/dt + a*d/dx.