Abstract
Liu and Jiao proposed a WLS-ENO method (Weighted-Least-Squares based Essentially Non-Oscillatory). Comparing to the WENO method (Weighted ENO), the WLS-ENO method is more flexible for solving the hyperbolic conservation laws. Notice that, a WLS problem is generated for each WLS-ENO procedure, although the QR factorization with column pivoting is employed, the computational cost of solving WLS problem is still heavy. So in this paper, we will propose an improved WLS-ENO method for improving the efficiency. The basic idea of new method is that, let the reconstructed polynomial approximate the cell averages of some smooth cells in conservation fashion, and approximate other cell averages in WLS fashion, so that the resulted WLS problem only has one unknown. Because the resulted WLS problem can be solved by using the normal equation directly, the whole computational cost is small, thus the new method has better efficiency.
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