水电站双线性调度规则研究

本文研究水电站水库调度函数问题。提出了用多种方法综合计算线性调度函数的方法 ,以使其更具稳定性。采用双线性调度函数相互印证和补充 ,给出了相应的计算公式 ,并提出了考虑各决策变量取值规律的具体决策规则。实例模拟调度得到了满意的结果 ,显示了所提双线性调度规则的有效性。

标量双曲型守恒方程初边值问题的一种数值解法

应用差分方法求双曲型守恒方程的数值解有很多缺点,例如:即使初值连续,也会产生不连续解.由此产生了激波及过超振荡现象.很多作者(LaxPD,HartenA,TadmorE,etal)都建立一些理论去处理它.但或多或少总还存在一些过超振荡现象,而且也不能应用于较长的时间层的计算.本文叙述了一种数值解法及其优点.克服了一些差分格式的缺点.也指出其不足之处,尚有待于进一步的探讨.

双曲型守恒律的一种三阶松弛格式

对一维双曲型守恒律,给出了一种形式更简单、计算量更小的三阶松弛格式.该格式以三阶WENO重构和三阶显隐式Runge-Kutta方法为基础.由于不用求解Riemann问题和计算非线性通量函数的雅可比矩阵,所以本文格式保持了松弛格式简单的优点.数值试验表明:该方法具有较高的分辨率.

A conservative local discontinuous Galerkin method for the solution of nonlinear Schrdinger equation in two dimensions

In this study, we present a conservative local discontinuous Galerkin(LDG) method for numerically solving the two-dimensional nonlinear Schrdinger(NLS) equation. The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux. The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central, alternative and upwind-based flux. We will propose two kinds of time discretization methods for the semi-discrete formulation. One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation. The other one is Krylov implicit integration factor(IIF) method which demands much less computational effort. Various numerical experiments are presented to demonstrate the conservation law of mass and energy, the optimal rates of convergence, and the blow-up phenomenon.

Implicit integration factor method for the nonlinear Dirac equation

A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.

Break Up of <i>N</i>-Soliton Bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity

We study the propagation of N-soliton bound state in a triangular gradient refractive index waveguide with nonlocal nonlinearity. The study is based on the direct numerical solutions of the model and subsequent eigenvalues evolution of the corresponding Zakharov-Shabat spectral problem. In the waveguide with local nonlinearity, the velocity of a single soliton is found to be symmetric around zero and therefore the soliton oscillates periodically inside the waveguide. If the nonlocality is presence in the medium, the periodic motion of soliton is destroyed due to the soliton experiences additional positive acceleration induced by the nonlocality. In the waveguide with the same strength of nonlocality, a higher amplitude soliton experiences higher nonlocality effects, i.e. larger acceleration. Based on this soliton behavior we predict the break up of N-soliton bound state into their single-soliton constituents. We notice that the splitting process does not affect the amplitude of each soliton component.

Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species

A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.

Predicting Solvent Concentration Profile in the Porous Media Using Various Numerical Solutions to Convection-Dispersion Equation

Convection-dispersion of fluids flowing through porous media is an important phenomenon in immiscible and miscible displacement in hydrocarbon reservoirs. Exact calculation of this problem leads to perform more robust reservoir simulation and reliable prediction. There are various techniques that have been proposed to solve convection-dispersion equation. To check the validity of these techniques, the convection-dispersion equation was solved numerically using a series of well known numerical techniques. Such techniques that employed in this study include method of line, explicit, implicit, Crank-Nicolson and Barakat-Clark. Several cases were considered as input, and convection-dispersion equation was solved using the aforementioned techniques. Moreover the error analysis was also carried out based on the comparison of numerical and analytical results. Finally it was observed that method of line and explicit methods are not capable of simulating the convection-dispersion equation for wide range of input parameters. The Barakat-Clark method was also failed to predict accurate results and in some cases it had large deviation from analytical solution. On the other hand, the simulation results of implicit and Crank-Nicolson have more qualitative and quantitative agreement with those obtained by the analytical solutions.

Discrete mass conservation and stability analysis of the ocean-atmosphere model with coupling conditions

In this work we considered bi-domain partial differential equations(PDEs)with two coupling interface conditions.The one domain is corresponding to the ocean and the second is to the atmosphere.The two coupling conditions are used to linked the interaction between these two regions.As we know that almost every engineering problem modeled via PDEs.The analytical solutions of these kind of problems are not easy,so we use numerical approximations.In this study we discuss the two essential properties,namely mass conservation and stability analysis of two types of coupling interface conditions for the oceanatmosphere model.The coupling conditions arise in general circulation models used in climate simulations.The two coupling conditions are the Dirichlet-Neumann and bulk interface conditions.For the stability analysis,we use the Godunov-Ryabenkii theory of normal-mode analysis.The main empha-sis of this work is to study the numerical properties of coupling conditions and an important point is to maintain conservativity of the overall scheme.Furthermore,for the numerical approximation we use two methods,an explicit and implicit couplings.The implicit coupling have further two algorithms,monolithic algorithm and partitioned iterative algorithm.The partitioned iterative approach is complex as compared to the monolithic approach.In addition,the comparison of the numerical results are exhibited through graphical illustration and simulation results are drafted in tabular form to validate our theoretical investigation.The novel characteristics of the findings from this paper can be of great importance in science and ocean engineering.

Optimal error estimates and modified energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell's equations

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.

An implicit parallel UGKS solver for flows covering various regimes

This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.

基于速度空间非结构网格和守恒修正的改进离散速度方法

传统离散速度方法在求解跨流域流动问题时,通常只求解动理学模型方程,即Boltzmann-BGK方程。与传统方法不同,改进离散速度方法同步求解了动理学模型方程和相应的宏观伴随方程。通过这种方式,可以将分子碰撞影响考虑到宏观伴随方程的通量计算中,同时宏观方程预估得到的结果可以用于预估平衡态,从而实现Boltzmann-BGK方程的全隐式离散。这两点改进可以有效克服传统方法在连续和近连续流区域计算效率低、计算精度差的缺陷。为了进一步减少速度空间的网格量和避免数值求积时的Runge现象,采用了非结构网格结合矩形律来离散速度空间并引进守恒修正来强制满足相容性条件。算例测试表明,采用速度空间非结构网格和守恒修正可以有效减少改进离散速度方法的计算量和内存花销。

EFFICIENT NUMERICAL ALGORITHMS FOR THREE-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional dif- fusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.

A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes

In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.