i am doing project on one dimensional gas exchange process in the manifolds of ic engine.

The gas exchange process is analysed usin the one dimensional conservation equation for mass , momemtum and energy.

i am applying the lax wendroff two step method for obtaining the temporal and spatial variation of pressure , velocity and density for the inner mesh point in the manifold ducts. At the inlet and out let to the cylinder the pipe boundary condition are determined using the mass , energy and momentum equation for conservation. Using these equation and finally reducing any one the equation to an equation of single variable, whose value is to be determined, and the remaining variables , which are known, am proceeding for iteration process by incrementing or decrementing the value of the required variable till the R.H.S of the equation equals to the L.H.S. I am sucessfully getting the results for the case of involved variable value of area ratio across the valve =1, when the valve is wide open.

BUT AS SOON AS I CHANGE THE VALUE OF AREA RATIO TO SOME LOWER VALUE LESS THAN ONE, WHICH HAS TO BE THERE FOR THE SIMULATION OF THE ENGINE CYCLE, THE FUNTION STOPS TO CONVERGE AFTER FEW TIME STEPS.

KINDLY GIVE ME ADVICE TO SOLVE THIS PROBLEM.

A Lax-Wendroff type of scheme is dispersive scheme. If you do the error analysis, you will find that the error terms are odd order terms. So it needs some kind of a damping term in it. This is called artificial damping. L-W scheme works well with pressure based artificial damping.

GB