On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes (Communications in Computational Physics, 2011)
In this paper we consider two commonly used classes of finite volumeweighted essentially non-oscillatory (WENO) schemes in two dimensional Cartesianmeshes. We compare them in terms of accuracy, performance for smooth and shockedsolutions, and efficiency in CPU timing. For linear systems both schemes are highorder accurate, however for nonlinear systems, analysis and numerical simulation resultsverify that one of them (Class A) is only second order accurate, while the other(Class B) is high order accurate. The WENO scheme in Class A is easier to implementand costs less than that in Class B. Numerical experiments indicate that the resolutionfor shocked problems is often comparable for schemes in both classes for the samebuilding blocks and meshes, despite of the difference in their formal order of accuracy.The results in this paper may give some guidance in the application of high order finitevolume schemes for simulating shocked flows.