extrapolation in MUSCL scheme

Chandra

hello,

I am planning to shift to MUSCL scheme in my Energy Equation solver(calculation of T) from upwind scheme (which I am using so far). I went through details and understood almost all the things except one, which is as follows:

To solve, say, "du/dt + df(u)/dx = 0", using MUSCL scheme, one needs to evaluate f[u*_(i+1/2)] and f[u*_(i-1/2)]. Literature says that u*_(i+1/2) = g[u_(1+1/2)_L, u_(1+1/2)_R] and u*_(i-1/2) = g[u_(1-1/2)_L, u_(1-1/2)_R].

For these functions "g()", the reference I got on wikipedia is to use Kurganov and Tadmor central scheme [http://en.wikipedia.org/wiki/MUSCL_scheme]. But that requires evaluation of spectral radius of "df/du" at different node-points to calculate the local propagation speed. This evaluation of spectral radius seems to be much time consuming.

Could any of you please suggest me any of the following:

1. How to evaluate the local-propagation speed "easily"?

2. Is there any other way to get a reliable function "g()" (instead of Kurganov and Tadmor's scheme).

and at last,

3. If I am wrong somewhere, please suggest me if there is any other way to implement the MUSCL scheme easily. Or, a way to have better solution than the upwind scheme I am using now (I thought of using 3rd order upwind scheme but I rejected the idea because it will get too complex on staggered, non-uniform grids).

Thank you very much in anticipation,

Please help me if you have any experience with using MUSCL,

regards, Chandra