An efficient improvement, based on the idea of homotopy, is proposed to improve and ensure the convergence of the modified Newton-Raphson (MNR) algorithm through the continuous mapping of solution space, and the behavior of solution is restrained towards the global convergence after several initial solution mappings. Comparisons of the new algorithm with MNR are presented, and the advantage of new algorithm is demonstrated for the problem of electrical impedance tomography.

An efficient improvement of modified Newton-Raphson algorithm for electrical impedance tomography

An efficient semi-implicit finite element model is proposed for the simulation of three-dimensional flows in stratified seas. The body of water is divided into a number of layers and the two horizontal momentum equations for each layer of water are first integrated vertically. Nine-node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain. The time derivatives are approximated using a second-order-accurate semi-implicit time-stepping scheme. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled. Two test cases for which analytic solutions are available are employed to test the proposed scheme. The test results show that the scheme is efficient and stable. A numerical experiment is also included to compare the proposed scheme with a finite difference scheme.

An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows

A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.

A coastal ocean model of semi-implicit finite volume unstructured grid

A semi-implicit finite element scheme is proposed for two-dimensional tidal flow computations. In the scheme, each term of the governing equations, rather than each dependent variable, is expanded in terms of the unknown nodal values and it helps to reduce computer execution time. The friction terms are represented semi-implicitly to improve stability, but this requires no additional computational effort. Test cases where analytic solutions have been obtained for the shallow water equations are employed to test the proposed scheme and the test results show that the scheme is efficient and stable. An numerical experiment is also included to compare the proposed scheme with another finite element scheme employing Serendipity-type Hermitian cubic basis functions. A numerical model of an actual bay is constructed based on the proposed scheme and computed tidal flows bear close resemblance to flows measured in field survey.

L. G. Chen

Papers

An efficient semi-implicit finite element scheme for two-dimensional tidal flow computations