Feng Xiao

Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows

Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called moments and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.

CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation

An accurate algorithm for the hyperbolic equations has been proposed by combining the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM) with the characteristic theory. Two types of moments, i.e. the point value (PV) at cell boundary of each mesh element and the volume-integrated average (VIA) over each mesh cell of a physical field, are treated as the model variables and updated independently in time. The interpolation that uses both PV and VIA is reconstructed for each Riemann invariant of the hyperbolic conservation laws. The PVs are then updated by semi-Lagrangian schemes along the characteristic curves, while the VIAs are computed by formulations of flux form, where the numerical fluxes are evaluated by averaging the physical fields over the characteristic curves. The Runge-Kutta type schemes are used for integrating the trajectory equations based on the characteristic speeds to improve the accuracy in time. The numerical procedure for the one-dimensional Euler conservation laws is described in detail in this paper. Number of benchmark tests are presented. The numerical results show that the present method is accurate and competitive to other existing methods.

Conservative Semi-Lagrangian Transport on a Sphere and the Impact on Vapor Advection in an Atmospheric General Circulation Model

Abstract A conservative semi-Lagrangian scheme with rational function for interpolation is implemented in spherical geometry and tested in an atmospheric general circulation model (AGCM). The new scheme, different from the conventional semi-Lagrangian method, is conservative and oscillation free. By introducing polar mixing and a time split computation of divergence, the scheme can compute advection transport correctly over the polar regions. Idealized advection tests with various velocity fields were carried out to demonstrate numerical accuracy and conservation in comparison with the spectral schemes. The impact of the advection computation on water vapor circulation in an AGCM is also investigated with numerical simulations on the Earth Simulator. Both pure advection tests and general circulation experiments show that the presented scheme is effective in improving the tracer transport property and the precipitation field in comparison with the leapfrog-spectral method.

Development of High Performance Simulator for Tsunami

Most of the existing numerical models for the simulation of Tsunami are based on the 2D shallow water equations. However, for many situations, it is necessary to use the 3D model in addition to the shallow water models to evaluate the damage in the coast region with a reliable accuracy. So, we propose the multi-scale warning system for Tsunami by coupling the 2D shallow water model and the 3D Navier-Stokes model that solves explicitly the free water surface to cover the physical phenomena that have diverse scales in both time and space. As a part of such a system, we, in this paper, present the essential numerics of the models based on the CIP/MM FVM (CIP/Multi-Moment Finite Volume Method) and some simulation results with the real geographical data for the 2D large-scale cases.

Three-phase flow calculation with conservative semi-Lagrangian CIP method

We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and sub-cell resolution including front capturing algorithm with functional transformation.Copyright