非理想爆源产生的爆炸场数值模拟

本文采用有限差分方法TVD(Total Variation Diminishing,A. Harten,1983)格式对非理想爆源在地面上形成的二维轴对称爆炸场进行了数值模拟,数值计算值与试验结果吻合得相当好。     

非理想爆源产生的爆炸场数值模拟

本文采用有限差分方法——TVD(Total Variation Diminishing,A. Harten,1983)格式对非理想爆源在地面上形成的二维轴对称爆炸场进行了数值模拟,数值计算值与试验结果吻合得相当好。     

基于MUSTA格式的全非线性Boussinesq波浪传播数值模型

建立了求解二维全非线性布氏（Boussinesq）水波方程的有限差分/有限体积混合数值格式. 针对守恒形式的控制方程,采用有限体积方法并结合 MUSTA格式计算数值通量, 剩余项则采用有限差分方法求解, 采用具有总变差减小（totalvariation diminishing, TVD）性质的三阶龙格-库塔法进行时间积分.该格式具备间断捕捉、程序实现简单、数值稳定性强、海岸动边界以及波浪破碎处理方便和可调参数少等优点.利用典型算例对数值模型进行了验证,计算结果与实验数据吻合较好.      

近似黎曼解对高超声速气动热计算的影响研究

高超声速流场计算一般采用TVD型格式,这些格式中,大多采用了不同形式的近似黎曼解. 通过分析和数值验证,论述了激波捕捉格式中近似黎曼解的耗散性质,说明其对高超声速热流计算的影响. 数值实验证明,采用低耗散格式可大大提高热流计算精度,降低热流计算对网格的依赖程度,从而获得精确的热流数值解.      

A FULLY NONLINEAR BOUSSINESQ MODELFOR WAVE PROPAGATION BASED ON MUSTA SCHEME

建立了求解二维全非线性布氏（Boussinesq）水波方程的有限差分/有限体积混合数值格式. 针对守恒形式的控制方程,采用有限体积方法并结合 MUSTA格式计算数值通量, 剩余项则采用有限差分方法求解, 采用具有总变差减小（totalvariation diminishing, TVD）性质的三阶龙格-库塔法进行时间积分.该格式具备间断捕捉、程序实现简单、数值稳定性强、海岸动边界以及波浪破碎处理方便和可调参数少等优点.利用典型算例对数值模型进行了验证,计算结果与实验数据吻合较好.     

驻定斜爆轰波并行数值模拟

采用多组分化学反应Euler方程组对驻定在高速飞行弹丸上的斜爆轰波流场进行了数值模拟。计算中分别采用TVD格式和基元反应模型,并基于并行编程模型MPI（message passing interface）实现了非结构网格上的并行计算,对流项和化学反应项用时间分裂法进行处理。计算结果表明并行计算能有效地提高计算速度,扩展计算规模,为进一步研究超驱爆轰推进技术奠定基础。     

TVD自相容流体力学拉氏格式研究

流体力学数值模拟格式总体上可分为Eulerian(欧氏)、Lagrangian(拉氏)和ALE(Arbitrary LagrangianEulerian),TVD广泛应用于Eulerian格式。本文利用具有TVD保持性质的Runge-Kutta型时间离散方法,构造了流体力学Lagrangian(拉氏)自相容格式,应用von Neumann小扰动技术分析了该格式的稳定性,并进行了相应的数值模拟,较好地抑制了激波波后非物理振荡。     

爆轰波平掠惰性气体界面及其解耦现象的数值研究

采用基元化学反应模型和迎风TVD格式,数值研究了爆轰波平掠惰性气体界面时的物理现象及其作用机制,并用点隐方法克服化学反应源项引起的计算刚性。数值结果显示,当爆轰波平掠过惰性气体界面时,形成了爆轰波、界面、透射激波以及稀疏波相互作用的现象。在高N2比例稀释的可燃混合气体情况下,当爆轰波平掠过特定惰性气体界面时,它与惰性气体界面相互作用产生的稀疏波可以导致爆轰波的解耦。     

基于非结构网格求解二维浅水方程的高精度有限体积方法

采用HLL格式,在三角形非结构网格下采用有限体积离散,建立了求解二维浅水方程的高精度的数值模型.本文采用多维重构和多维限制器的方法来获得高精度的空间格式以及防止非物理振荡的产生,时间离散采用三阶Runge-Kutta法以获得高阶的时间精度.基于三角形网格,底坡源项采用简单的斜底模型离散,为保证计算格式的和谐性,对经典的HLL格式计算的数值通量中的静水压力项进行了修正.算例证明本文提出的方法的和谐性并具有高精度的间断捕捉能力和稳定性.     

一维孔隙率浅水方程及其数值离散

通过孔隙率方法来描述挡水物对过水能力的影响建立了一维孔隙率浅水方程. 采用有限体积方法和Roe格式的近似Riemann解建立了孔隙率浅水方程的离散模式. 对底坡和孔隙率源项采用特性方向分解的方法进行处理,使模型精确满足C(Conservative)特性,增加了模型的稳定性. 通过算例模拟证明了模型可以对河道中的挡水物作用进行模拟,且计算结果表明模型具有和谐、稳定、分辨率高等优点.      

求解浅水波方程的半离散中心迎风方法

将Jin's的界面方法应用到求解双曲守恒型方程的半离散中心迎风方法中,给出了一种新的求解浅水波方程的半离散中心迎风差分方法。对于源项,不是采用传统的单元均值而是采用单元界面处的值来近似,使所得格式对稳定态的求解是均衡的。且已证明所给的二阶精度的求解格式保持水深的非负性,这一特性使其能够较好的处理干河床问题。使用该方法产生的数值粘性(与O(Δ2r-1)同阶)要比交错的中心格式小(与O(Δx2r/Δt)同阶),而且由于数值粘性与时间步长无关,从而时间步长可根据稳定性需要尽可能的小,因此适用于稳定态的求解。     

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

This paper comprises an implementation of a fourth‐order Runge–Kutta discontinuous Galerkin (RKDG4) scheme for computing the open‐channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high‐order slope limiting procedure, and high‐order source terms approximations. A comparison of the performance of the proposed method with lower‐order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high‐order model. Copyright © 2008 John Wiley & Sons, Ltd.     

基于WENO-THINC/WLIC模型的水气二相流数值模拟

水气二相流与诸多领域的实际工程问题密切相关. 对二相流运动进行高精度的数值模拟是计算流体力学研究的难点和热点. 针对开敞水域的自由表面流运动问题, 将水和空气均视为不可压缩流体, 采用五阶加权基本无震荡(weighted essentially non-oscillatory, WENO)格式求解描述流体运动的纳维斯托克斯(Navier-Stokes, NS)方程, 利用以加权线性界面算法改进的多维双曲正切函数界面捕捉法(tangent of hyperbola for interface capturing with weighed line interface calculation, THINC/WLIC)追踪水气界面, 建立WENO-THINC/WLIC水气二相流运动数值模型. 模型采用分步计算法离散求解控制方程, 通过压力投影法求解压强场, 并利用三阶总变差递减(total variation diminishing, TVD)龙格库塔(Runge-Kutta, RK)法对时间项进行离散求解. 通过对环境速度场下Zalesak's disk和shearing vortex界面运动问题, 线性液舱晃荡问题以及溃坝问题的模拟结果与理论分析或试验结果的比较, 对所建立的水气二相流数值模型的适用性及模拟精度进行了验证. 结果表明, 本模型的模拟结果与物理模型或理论分析结果吻合良好, 能较为准确地再现不可压缩水气二相流运动现象. 鉴于WENO格式和THINC法本身在算法及应用等方面仍在不断改进, 本研究提出的WENO-THINC耦合模型为后续更高精度的二相流计算模型开发提供了一种研究思路.      

A γ‐DGBGK scheme for compressible multi‐fluids

The paper presents a Discontinuous Galerkin γ‐BGK (γ‐DGBGK) method for compressible multicomponent flow simulations by coupling the discontinuous Galerkin method with a γ‐BGK scheme based on WENO limiters. In this γ‐DGBGK method, the construction of the flux in the DG method is based on the kinetic scheme which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous terms in the flux formulation at cell interfaces. WENO limiters are used to obtain uniform high‐order accuracy and sharp non‐oscillatory shock transition, and time accuracy obtained by integration for the flux function at the cell interface. Numerical examples in one and two space dimensions are presented to illustrate the robust and accuracy of the present scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

A combined level set/ghost cell immersed boundary representation for floating body simulations

A six degrees of freedom (6DOF) algorithm is implemented in the open‐source CFD code REEF3D. The model solves the incompressible Navier–Stokes equations. Complex free surface dynamics are modeled with the level set method based on a two‐phase flow approach. The convection terms of the velocities and the level set method are treated with a high‐order weighted essentially non‐oscillatory discretization scheme. Together with the level set method for the free surface capturing, this algorithm can model the movement of rigid floating bodies and their interaction with the fluid. The 6DOF algorithm is implemented on a fixed grid. The solid‐fluid interface is represented with a combination of the level set method and ghost cell immersed boundary method. As a result, re‐meshing or overset grids are not necessary. The capability, accuracy, and numerical stability of the new algorithm is shown through benchmark applications for the fluid‐body interaction problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Verification of Euler/Navier–Stokes codes using the method of manufactured solutions

The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes. The Premo code employs a node‐centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second‐order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.     

Parallel three‐dimensional simulation of the injection molding process

This paper describes the development of a parallel three‐dimensional unstructured non‐isothermal flow solver for the simulation of the injection molding process. The numerical model accounts for multiphase flow in which the melt and air regions are considered to be a continuous incompressible fluid with distinct physical properties. This aspect avoids the complex reconstruction of the interface. A collocated finite volume method is employed, which can switch between first‐ and second‐order accuracy in both space and time. The pressure implicit with splitting of operators algorithm is used to compute the transient flow variables and couple velocity and pressure. The temperature equation is solved using a transport equation with convection and diffusion terms. An upwind differencing scheme is used for the discretization of the convection term to enforce a bounded solution. In order to capture the sharp interface, a bounded compressive high‐resolution scheme is employed. Parallelization of the code is achieved using the PETSc framework and a single program multiple data message passing model. Predicted numerical solutions for several example problems are considered. The first case validates the solution algorithm for moderate Reynolds number flows using a structured mesh. The second case employs an unstructured hybrid mesh showing the capability of the solver to describe highly viscous flows closer to realistic injection molding conditions. The final case presents the non‐isothermal filling of a thick cavity using three mesh sizes and up to 80 processors to assess parallel performance. The proposed algorithm is shown to have good accuracy and scalability. Copyright © 2008 John Wiley & Sons, Ltd.     

A split operator scheme for ocean wave simulation

A coupled discrete spectral model was developed for the prediction of ocean waves by solving the energy conservation equation of the two-dimensional wave spectrum. The model includes the dispersion correction terms in the governing equation to account for the dispersive effect due to the frequency-dependent velocities of waves. A split operator scheme is used to deal with the numerical problems arising from different terms of the governing equation. The advection terms are solved by the proven accurate minimax characteristics method to avoid excessive numerical damping or oscillations. The dispersion correction terms are solved by central differencing. The source and sink terms are solved by a quasi-second-order explicit scheme with limitation on energy growth per time step to allow the use of a large time step. The model was verified by ideal test cases and wave-hindcasting studies under typhoon conditions in the South China Sea near Hong Kong.     

Finite‐volume multi‐stage schemes for shallow‐water flow simulations

A finite‐volume multi‐stage (FMUSTA) scheme is proposed for simulating the free‐surface shallow‐water flows with the hydraulic shocks. On the basis of the multi‐stage (MUSTA) method, the original Riemann problem is transformed to an independent MUSTA mesh. The local Lax–Friedrichs scheme is then adopted for solving the solution of the Riemann problem at the cell interface on the MUSTA mesh. The resulting first‐order monotonic FMUSTA scheme, which does not require the use of the eigenstructure and the special treatment of entropy fixes, has the generality as well as simplicity. In order to achieve the high‐resolution property, the monotonic upstream schemes for conservation laws (MUSCL) method are used. For modeling shallow‐water flows with source terms, the surface gradient method (SGM) is adopted. The proposed schemes are verified using the simulations of six shallow‐water problems, including the 1D idealized dam breaking, the steady transcritical flow over a hump, the 2D oblique hydraulic jump, the circular dam breaking and two dam‐break experiments. The simulated results by the proposed schemes are in satisfactory agreement with the exact solutions and experimental data. It is demonstrated that the proposed FMUSTA schemes have superior overall numerical accuracy among the schemes tested such as the commonly adopted Roe and HLL schemes. Copyright © 2007 John Wiley & Sons, Ltd.     

A robust high‐resolution finite volume scheme for the simulation of long waves over complex domains

The propagation, runup and rundown of long surface waves are numerically investigated, initially in one dimension, using a well‐balanced high‐resolution finite volume scheme. A conservative form of the nonlinear shallow water equations with source terms is solved numerically using a high‐resolution Godunov‐type explicit scheme coupled with Roe's approximate Riemann solver. The scheme is also extended to handle two‐dimensional complex domains. The numerical difficulties related to the presence of the topography source terms in the model equations along with the appearance of the wet/dry fronts are properly treated and extended. The resulting numerical model accurately describes breaking waves as bores or hydraulic jumps and conserves volume across flow discontinuities. Numerical results show very good agreement with previously presented analytical or asymptotic solutions as well as with experimental benchmark data. Copyright © 2007 John Wiley & Sons, Ltd.