A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, a new fifth-order finite volume central weighted essentiallynon-oscillatory (CWENO) scheme is proposed for solving hyperbolic conservationlaws on staggered meshes. The high-order spatial reconstruction procedure usinga convex combination of a fourth degree polynomial with two linear polynomials(in one dimension) or four linear polynomials (in two dimensions) in a traditionalWENO fashion and a time discretization method using the natural continuous extension (NCE) of the Runge-Kutta method are applied to design this new fifth-orderCWENO scheme. This new finite volume CWENO scheme uses the information defined on the same largest spatial stencil as that of the same order classical CWENOschemes [37, 46] with the application of smaller number of unequal-sized spatial stencils. Since the new nonlinear weights are adopted, the new finite volume CWENOscheme could obtain the same order of accuracy and get smaller truncation errors in $L^1$ and $L^∞$ norms in smooth regions, and control the spurious oscillations near strongshocks or contact discontinuities. The new CWENO scheme has advantages over theclassical CWENO schemes [37, 46] on staggered meshes in its simplicity and easy extension to multi-dimensions. Some one-dimensional and two-dimensional benchmarknumerical examples are provided to illustrate the good performance of this new fifth-order finite volume CWENO scheme.