求解二维浅水流动方程的Godunov格式

采用网格变换和Strang算子分裂,以准确Riemann解为基础。建立了求解非平底浅水流动方程的Godunov格式,用“水位方程法（Water Level Formulation)”求Riemann解,结合中心差分和Riemann解离散底坡项,保证了计算格式的和谐性,经验证,方法健全。通用,且分辨率高。     

A multi-purpose Schrödinger-Poisson Solver for TCAD applications

We present the Vienna Schrödinger-Poisson Solver (VSP), a multi-purpose quantum mechanical solver for investigations on nano-scaled device structures. VSP includes a quantum mechanical solver for closed as well as open boundary problems on fairly arbitrary one-dimensional cross sections within the effective mass framework. For investigations on novel gate dielectrics VSP holds models for bulk and interface trap charges, and direct and trap assisted tunneling. Hetero-structured semiconductor devices, like resonant tunneling diodes (RTD), can be treated within the closed boundary model for quick estimation of resonant energy levels. The open boundary model allows evaluation of current voltage characteristics.     

基于网格平均的跟踪法应用于Euler方程组

设计了一种求解Euler方程组的基于网格平均框架的守恒型激波跟踪法,算例表明利用该方法求解守恒方程组的数值解很有效,并且编制程序相对容易,尤其是能给出很精确的间断位置。     

k‐version of finite element method in gas dynamics: higher‐order global differentiability numerical solutions

In this paper, we consider and examine alternate finite element computational strategies for time‐dependent Navier–Stokes equations describing high‐speed compressible flows with shocks in a viscous and conducting medium, with the ultimate objective of establishing the desired features of a general mathematical and computational framework for such initial value problems (IVP) in which: (a) the numerically computed solutions are in agreement with the physics of evolution described by the governing differential equations (GDEs) i.e. the IVP, (b) the solutions are admissible in the non‐discretized form of the GDEs in the pointwise sense (i.e. anywhere and everywhere) in the entire space–time domain, and hence in the integrated sense as well, (c) the numerical approximations progressively approach the same global differentiability in space and time as the theoretical solutions, (d) it is possible to time march the solutions (this is essential for efficiency as well as ensuring desired accuracy of the computed solution for the current increment of time, i.e. to minimize the error build up in the time marching process), (e) the computational process is unconditionally stable and non‐degenerate regardless of the choice of discretization, nature of approximations and their global differentiability and the dimensionless parameters influencing the physics of the process, (f) there are no issues of stability, CFL number limitations and (g) the mathematical and computational methodology is independent of the nature of the space–time differential operators. We consider one‐dimensional compressible flow in a viscous and conducting medium with shocks as model problems to illustrate various features of the general mathematical and computational framework used here and to demonstrate that the proposed framework is general and is applicable to all IVP. The Riemann shock tube with a single diaphragm serves as a model problem. The specific details presented in the paper discuss: (1) Choice of the form of the GDEs, i.e. strong form or weak form. (2) Various choices of variables. The paper establishes and considers density, velocity and temperature as variables of choice. (3) Details of the space–time least squares (LS) integral forms (meritorious over all others in all aspects) are presented and choice of approximation spaces are discussed. (4) In all numerical studies we consider a viscous and conducting medium with ideal gas law, however results are also presented for non‐conducting medium. Extension of this work to real gas models will be presented in a separate paper. It is worth noting that when the medium is viscous and conducting, the solutions of gas dynamics equations are analytic. (5) It is also significant to note that upwinding methods based on addition of artificial diffusion such as SUPG, SUPG/DC, SUPG/DC/LS and their many variations are neither needed nor used in this present work. (6) Numerical studies are aimed at resolving the localized details of the shock structure, i.e. shock relations, shock width, shock speed, etc. as well as the over all global behaviour of the solution in the entire space–time domain. (7) Numerical studies are presented for Riemann shock tube for high Mach number flows with special emphasis also on time accuracy of the evolution which is ensured by requiring that the approximations for each increment of time satisfy non‐discretized form of the GDEs in the pointwise sense, and hence in the integrated sense as well. (8) Comparisons are made with published results as well as theoretical solutions (when possible). It is established that space–time least squares processes are the only processes that yield variationally consistent space–time integral forms, and hence unconditionally non‐degenerate space–time computational processes, which when considered in higher‐order scalar product spaces provide the desired mathematical framework in which progressively higher‐order global differentiability solutions in space and time yield the same characteristics as the theoretical solutions of the IVP in all aspects. Copyright © 2006 John Wiley & Sons, Ltd.     

An analysis of dam-break flow on slope

The one-dimensional steep slope shallow water equations are used to model the dam-break flow down a uniform slope with arbitrary inclination, and analytical solutions are derived by the hodograph transformation and the Riemann＇s method in terms of evaluated integrals. An implicit analytical solution is obtained to evaluate the spatio-temporal distributions of dam-break flood hydrographs along the slope. For convenience, the solution for representative wave profiles and velocity distributions is shown in charts. Comparing with the Dressler＇s solution and WES experimental data, the analytical solution is seen reasonable.     

Numerical computations of resistance of high speed catamaran in calm water

In this paper, the in-house multifunction solver naoe-FOAM-SJTU is applied to study the resistance and wave-making performance of a high-speed catamaran sailing at different velocity in calm water. The volume of fluid（VOF） method is used to capture the free interface and the finite volume method（FVM） is adopted as the discretization scheme. The hull model is fixed with initial trim and sinkage. The numerical results of the presented paper agree very well with the measurement data of model test. Wave making and vortex field are well simulated to analyze the hydrodynamic performance of a catamaran.     

非结构网格的并行多重网格解算器

多重网格方法作为非结构网格的高效解算器,其串行与并行实现在时空上都具有优良特性.以控制方程离散过程为切入点,说明非结构网格在并行数值模拟的流程,指出多重网格方法主要用于求解时间推进格式产生的大规模代数系统方程,简述了算法实现的基本结构,分析了其高效性原理;其次,综述性地概括了几何多重网格与代数多种网格研究动态,并对其并行化的热点问题进行重点论述.同时,针对非结构网格的实际应用,总结了多重网格解算器采用的光滑算子;随后列举了非结构网格应用的部分开源项目软件,并简要说明了其应用功能;最后,指出并行多重网格解算器在非结构网格应用中的若干关键问题和未来的研究方向.     

Numerical Simulation of Fluid-Structure Interaction Using Modified Ghost Fluid Method and Naviers Equations

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann problem is defined and a nonlinear characteristic from the fluid and a Riemann invariant from the solid are used to predict and define the ghost fluid states. Theoretical analysis shows that the present approach is accurate in the sense of approximating the solution of the Riemann problem at the interface. Numerical validation of this approach is also accomplished by extensive comparison to 1D problems (both water-solid and gas-solid) with their respective analytical solutions. T.G. Liu’s current address: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083. email: liutg@buaa.edu.cn.     

A numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algorithm

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [J. Comp. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible Newtonian fluid, and the flow is fully developed. The flow rate (flux) is considered as a periodic function of time (prescribed). The axial pressure gradient and velocity distribution in the eccentric catheterized artery are obtained as solutions of the problem. Through the computed results on axial pressure gradient, the increases in mean pressure gradient and frictional resistance in the artery due to catheterization are estimated. These estimates can be used to correct the error involved in the measured pressure gradients using catheters.     

NUMERICAL SIMULATION OF VISCOUS FLOW AROUND AN APPENDED SUBMARINE MODEL

A multizone/multiblock coupled RANS equation solver is presented to numerically simulate the viscous flow around an appended submarine model at Reynolds number 1. E7. k-ε two equation turbulenc model together with wall function are used. The resulting finite difference equations are solved by SIMPLEC, ADI. The technique of rising up the bottom surface is presented to overcome radial contraction problem in Cartesian coordinate system. Benchmark numerical calculations have been compared with experimental data, the radial distribution of axial velocity on the propeller disk plane is 4. 63%.