WENO families in accuracy and computational costs

In this paper a comparison of Weighted Essentially Non-Oscillatory (WENO) scheme is presented and different kinds are compared. High resolution schemes are one of the best ways decreasing the cost of processes and also increasing the resolution as is clear. Different WENO’s influence on the weights that applies on the neighborhood of the cells that is supposing to be calculated. Mentioned schemes, were tested on wave equation at first and in continued with the first and second dimension test cases. 3rd ,5th, 7th and 9th order of JS-WENO, MWENO, ZWENO and MZWENO are compared in Goethe tests. This scheme was applied in finite volume characteristic wise algorithm in order to reach much more accuracy. Buckley-Leverette, Sod shock tube, Shu-Osher, Lax test, Riley-Taylor instability and double Mach reflection test cases was compared. As the result, MZWENO in equal order with the other ones would report more accurate reply. But as a new research here we showed that e.g. although MZWENO 5th order could promote the accuracy of the scheme up to about two times higher, but the cost of computing will increase more than the JS 7th order one. So, it is concluded that employing 7th order of JS-WENO leads to higher accuracy with less computational costs.

کلیدواژه ها:

WENO ، Characteristic ، finite volume ، Lax Friedrich flux splitting ، computational costs