Semi-explicit methods for isospectral flows

University of Cambridge Semi-explicit Methods for Isospectral Ows Semi-explicit Methods for Isospectral Ows

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L 0 = B; L] for d d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying ow. We present techniques that allow us to decrease the breakd...

Numerical solution of isospectral flows

In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation L′ = [B(L), L], L(0) = L0, where L0 is a d × d symmetric matrix, B(L) is a skew-symmetric matrix function of L and [B,L] is the Lie bracket operator. We show that standard Runge–Kutta schemes fail in recovering the main qualitative feature of these...

University of Cambridge Lie-group Methods for Isospectral Flows

A case study of flood dynamic wave simulation in natural waterways using numerical solution of unsteady flows

Flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. Floods are taken unsteady flows that vary by time and location. Equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the Saint-Venant hypothesis is considered. Dynamic wave model as ...

Combination of Adaptive-Grid Embedding and Redistribution Methods on Semi Structured Grids for two-dimensional invisid flows

Among the adaptive-grid methods, redistribution and embedding techniques have been the focus of more attention by researchers. Simultaneous or combined adaptive techniques have also been used. This paper describes a combination of adaptive-grid embedding and redistribution methods on semi-structured grids for two-dimensional invisid flows. Since the grid is semi-structured, it is possible to us...