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A. P. Engsig‐Karup 《国际流体数值方法杂志》2014,74(10):749-773
Robust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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A new accurate finite‐difference (AFD) numerical method is developed specifically for solving high‐order Boussinesq (HOB) equations. The method solves the water‐wave flow with much higher accuracy compared to the standard finite‐difference (SFD) method for the same computer resources. It is first developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Padé approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate solution is found to be excellent compared to the SFD solution. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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This paper presents a parametric finite‐difference scheme concerning the numerical solution of the one‐dimensional Boussinesq‐type set of equations, as they were introduced by Peregrine (J. Fluid Mech. 1967; 27 (4)) in the case of waves relatively long with small amplitudes in water of varying depth. The proposed method, which can be considered as a generalization of the Crank‐Nickolson method, aims to investigate alternative approaches in order to improve the accuracy of analogous methods known from bibliography. The resulting linear finite‐difference scheme, which is analysed for stability using the Fourier method, has been applied successfully to a problem used by Beji and Battjes (Coastal Eng. 1994; 23 : 1–16), giving numerical results which are in good agreement with the corresponding results given by MIKE 21 BW (User Guide. In: MIKE 21, Wave Modelling, User Guide. 2002; 271–392) developed by DHI Software. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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This paper presents the results of some studies on the development and application of a finite element method (FEM) with a closed-form solution technique for time discretization. The closed-form solution is based on the eigenvalues/vectors of a coefficient matrix. The method is first applied to the one-dimensional linearized shallow water equations and then extended to the two-dimensional shallow water equations. An attempt is made to improve its efficiency by incorporating time splitting and using the closed-form solution technique only for linear terms. Some case studies of a rectangular channel and harbour are presented to illustrate the satisfactory working of the method. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 953–963, 1997. 相似文献
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A further development of the QALE‐FEM (quasi‐arbitrary Lagrangian–Eulerian finite element method) based on a fully nonlinear potential theory is presented in this paper. This development enables the QALE‐FEM to deal with three‐dimensional (3D) overturning waves over complex seabeds, which have not been considered since the method was devised by the authors of this paper in their previous works (J. Comput. Phys. 2006; 212 :52–72; J. Numer. Meth. Engng 2009; 78 :713–756). In order to tackle challenges associated with 3D overturning waves, two new numerical techniques are suggested. They are the techniques for moving the mesh and for calculating the fluid velocity near overturning jets, respectively. The developed method is validated by comparing its numerical results with experimental data and results from other numerical methods available in the literature. Good agreement is achieved. The computational efficiency of this method is also investigated for this kind of wave, which shows that the QALE‐FEM can be many times faster than other methods based on the same theory. Furthermore, 3D overturning waves propagating over a non‐symmetrical seabed or multiple reefs are simulated using the method. Some of these results have not been found elsewhere to the best of our knowledge. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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A methodology for computing three‐dimensional interaction between waves and fixed bodies is developed based on a fully non‐linear potential flow theory. The associated boundary value problem is solved using a finite element method (FEM). A recovery technique has been implemented to improve the FEM solution. The velocity is calculated by a numerical differentiation technique. The corresponding algebraic equations are solved by the conjugate gradient method with a symmetric successive overrelaxation (SSOR) preconditioner. The radiation condition at a truncated boundary is imposed based on the combination of a damping zone and the Sommerfeld condition. This paper (Part 1) focuses on the technical procedure, while Part 2 [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 2. Numerical results and validation. International Journal for Numerical Methods in Fluids 2001] gives detailed numerical results, including validation, for the cases of steep waves interacting with one or two vertical cylinders. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM‐type equation. Explicit and implicit–explicit Runge–Kutta‐type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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ＳＰＬＩＴＴＩＮＧＭＥＴＨＯＤＦＯＲＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＰＨＲＥＡＴＩＣＦＬＯＷＥＱＵＡＴＩＯＮＸｕＳｈａｏｈｕｉ（徐绍辉）ＺｈｕＸｕｅｙｕ（朱学愚）ＺｈｕＧｕｏｒｏｎｇ（朱国荣）（ＲｅｃｅｉｖｅｄＭａｙ１１,１９９５;Ｃｏｍｍｕｎｉｃａｔ... 相似文献
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A new hybrid model, which is based on domain decomposition and proposed by the authors, is used for calculating the flow around
a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2−18) respectively. The vortex motion patterns in asymmetric regime, single pair (or transverse) regime and double pair (or
diagonal) regime are successfully simulated. The calculated drag and inertial force coefficients are in better agreement with
experimental data than other recent computational results.
The project supported by the National Natural Science Foundations of China and the LNM, Institute of Mechanics, Academia Sinica 相似文献
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This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision. 相似文献
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Huang Yuying Yue Dongyi Qian Qin 《Acta Mechanica Solida Sinica》1995,8(4):337-348
A reciprocal theorem of dynamics for potential flow problems is first derived by meansof the Laplace transform in which the compressibility of water is taken into account.Based on this the-orem,the corresponding time-space boundary integral equation is obtained.Then,a set of time do-main boundary element equations with recurrence form is immediately formulated through discretiza-tion in both time and boundary.After having carried out the numerical calculation two solutions arefound in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impacton the surface of a half-space fluid.The results show that the present method is more efficient than theprevious ones. 相似文献
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This work is concerned with a study of container filling, with particular reference to the food industry. A computer code was developed and an experimental rig was built, the main purpose being to validate the software. The computational fluid dynamic (CFD) code, called GENSMAC, was specifically designed for relatively slow viscous flow and was capable of capturing multiple free surfaces. This paper focuses on the design of the experimental rig and how it functions. The visual output of the code is then compared with high‐speed photographic shots of glucose syrup being jetted into a tub for a selected number of flow regimes. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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Yanbao Ma Chien‐Pin Sun David A. Haake Bernard M. Churchill Chih‐Ming Ho 《国际流体数值方法杂志》2012,70(6):703-712
A high‐order alternating direction implicit (ADI) method for solving the unsteady convection‐dominated diffusion equation is developed. The fourth‐order Padé scheme is used for the discretization of the convection terms, while the second‐order Padé scheme is used for the diffusion terms. The Crank–Nicolson scheme and ADI factorization are applied for time integration. After ADI factorization, the two‐dimensional problem becomes a sequence of one‐dimensional problems. The solution procedure consists of multiple use of a one‐dimensional tridiagonal matrix algorithm that produces a computationally cost‐effective solver. Von Neumann stability analysis is performed to show that the method is unconditionally stable. An unsteady two‐dimensional problem concerning convection‐dominated propagation of a Gaussian pulse is studied to test its numerical accuracy and compare it to other high‐order ADI methods. The results show that the overall numerical accuracy can reach third or fourth order for the convection‐dominated diffusion equation depending on the magnitude of diffusivity, while the computational cost is much lower than other high‐order numerical methods. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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This paper presents a new spectral model for solving the fully nonlinear potential flow problem for water waves in a single horizontal dimension. At the heart of the numerical method is the solution to the Laplace equation which is solved using a variant of the ‐transform. The method discretizes the spatial part of the governing equations using the Galerkin method and the temporal part using the classical fourth‐order Runge‐Kutta method. A careful investigation of the numerical method's stability properties is carried out, and it is shown that the method is stable up to a certain threshold steepness when applied to nonlinear monochromatic waves in deep water. Above this threshold artificial damping may be employed to obtain stable solutions. The accuracy of the model is tested for: (i) highly nonlinear progressive wave trains, (ii) solitary wave reflection, and (iii) deep water wave focusing events. In all cases it is demonstrated that the model is capable of obtaining excellent results, essentially up to very near breaking. 相似文献
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为高效和高精度求解长距离输水系统瞬变流变化过程,应用三阶ENO有限体积格式求解一维管道非恒定流方程组,基于Lax-Friedrichs通量裂分法重构界面通量,上下游界面采用虚拟网格技术并结合交叉管网边界条件建立了一套高效和高精度求解管道瞬变流水锤波的数值模型。引入GPU加速技术,实现对大型输水系统的高效计算。通过特征线法、一阶及二阶Godunov有限体积格式对模型进行验证,结果表明,三阶ENO格式在极低的Courant数时也能保持较好的间断捕捉性能且无非物理振荡。同时,对Courant数的高度不敏感性,使得模型划分网格时具有高度的灵活性并能显著提高计算速度。应用GPU加速技术,发现模型在较多网格数时有明显的加速效果,且加速效果随网格数增多而显著。本文模型可为长距离输水系统非恒定瞬变过程的高效精准快速模拟预测提供理论支撑。 相似文献
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A new modified Galerkin/finite element method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low‐order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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时域边界元法分析撞水响应 总被引：6，自引：1，他引：6
基于势流理论，考虑流场的可压缩性，首先利用积分变换导得了势流问题的一个动力学倒易定理，在此基础上，进而求得问题对应的时空边界积分方程，然后通过对边界和时间轴同时离散，建立了一组有递推形式的时间边界元方程最后结合液面条件和物体运动方程耦全求解得到了刚体的撞水响应。 相似文献