Implicit methods for two-dimensional unsteady free-surface flows

Fennema, Robert J.; Chaudhry, M. Hanif

doi:10.1080/00221688909499167

Cited by 68 publications

(23 citation statements)

References 4 publications

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“…The solution for shear flow problem with MOVERS-1 variant is almost identical to that of n-variant (figure 7) and hence is not reproduced here. The scheme is used to solve flow over a forward-facing step in wind tunnel and the slip lines starting at the Mach stem from right above the step are clearly seen in figure (36). The computation with unstructured mesh is also found accurate as evident in the solution for hypersonic flow across a half cylinder presented in figure (37).…”

Section: Results With Movers-1 For Euler Equationsmentioning

confidence: 87%

“…This problem corresponds to a partial breach [36] and detailed in figure 20. The Numerical results displaying 3D views of the water surface elevation after dam failure and velocity contours at time t=7.2 seconds are presented in figure (21) and that for steady oblique hydraulic jump compared with LLF scheme is depicted in figure (22).…”

Section: D Partial Dam Break Problemmentioning

confidence: 99%

“…This problem corresponds to a partial breach [36]. Consider a 2D partial dambreak problem with an unsymmetrical breach.…”

Section: D Partial Dam Break Problemmentioning

confidence: 99%

“…where α LLF is the local maximum of the spectral radius of the flux Jacobian matrix and α M OV ERS is the corrected wave speed obtained using MOVERSn(or 1) (see the expressions (33) to (36) in the following subsection), using the R-H condition. Here, φ is a standard limiter.…”

Section: Movers-lmentioning

confidence: 99%

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A central Rankine–Hugoniot solver for hyperbolic conservation laws

Jaisankar

Rao

2009

Journal of Computational Physics

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A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical method. The basic idea is to fix the coefficient of numerical dissipation based on the Rankine-Hugoniot (jump) condition. Several numerical examples for scalar and vector hyperbolic conservation laws representing the inviscid Burgers equation, the Euler equations of gas dynamics, shallow water equations and ideal MHD equations in one and two dimensions are presented which demonstrate the efficiency and accuracy of this numerical method in capturing the flow features.

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Section: Results With Movers-1 For Euler Equationsmentioning

confidence: 87%

Section: D Partial Dam Break Problemmentioning

confidence: 99%

“…This problem corresponds to a partial breach [36]. Consider a 2D partial dambreak problem with an unsymmetrical breach.…”

Section: D Partial Dam Break Problemmentioning

confidence: 99%

Section: Movers-lmentioning

confidence: 99%

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A central Rankine–Hugoniot solver for hyperbolic conservation laws

Jaisankar

Rao

2009

Journal of Computational Physics

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“…The finite difference 606 Y. ZHANG, Z. ZENG AND J. CHEN methods with the MacCormack scheme [4], and the Gabutti scheme [5], the approximate Riemann solvers [6], the modified Lax-Friedrich scheme [7], Beam-Warming scheme and its modifications [8,9], the total variation diminishing (TVD) scheme [10,11], and the central scheme [12] were also applied. Additionally, the finite element method using the Eulerian-Lagrangian linked Galerkin scheme [13], the dissipative Galerkin scheme [14,15], Petrov-Galerkin scheme [16] appeared in the literature.…”

Section: Introductionmentioning

confidence: 99%

The improved space–time conservation element and solution element scheme for two‐dimensional dam‐break flow simulation

Zhang

Zeng

Chen

2011

Numerical Methods in Fluids

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SUMMARYA new numerical scheme, namely space-time conservation element and solution element (CE/SE) method, has been used for the solution of the two-dimensional (2D) dam-break problem. Distinguishing from the well-established traditional numerical methods (such as characteristics, finite difference, finite element, and finite-volume methods), the CE/SE scheme has many non-traditional features in both concept and methodology: space and time are treated in a unified way, which is the most important characteristic for the CE/SE method; the CEs and SEs are introduced, both local and global flux conservations in space and time rather than space only are enforced; an explicit scheme with a stagger grid is adopted. Furthermore, this scheme is robust and easy to implement. In this paper, an improved CE/SE scheme is extended to solve the 2D shallow water equations with the source terms, which usually plays a critical role in dam-break flows. To demonstrate the accuracy, robustness and efficiency of the improved CE/SE method, both 1D and 2D dam-break problems are simulated numerically, and the results are consistent with either the analytical solutions or experimental results.

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Depth-averaged two-dimensional curvilinear explicit finite analytic model for open-channel flows

Hsu

Yeh

Yang

2000

Int. J. Numer. Meth. Fluids

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A depth‐averaged two‐dimensional model has been developed in the curvilinear co‐ordinate system for free‐surface flow problems. The non‐linear convective terms of the momentum equations are discretized based on the explicit–finite–analytic method with second‐order accuracy in space and first‐order accuracy in time. The other terms of the momentum equations, as well as the mass conservation equation, are discretized by the finite difference method. The discretized governing equations are solved in turn, and iteration in each time step is adopted to guarantee the numerical convergence. The new model has been applied to various flow situations, even for the cases with the presence of sub‐critical and supercritical flows simultaneously or sequentially. Comparisons between the numerical results and the experimental data show that the proposed model is robust with satisfactory accuracy. Copyright © 2000 John Wiley & Sons, Ltd.

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Implicit methods for two-dimensional unsteady free-surface flows

Cited by 68 publications

References 4 publications

A central Rankine–Hugoniot solver for hyperbolic conservation laws

A central Rankine–Hugoniot solver for hyperbolic conservation laws

The improved space–time conservation element and solution element scheme for two‐dimensional dam‐break flow simulation

Depth-averaged two-dimensional curvilinear explicit finite analytic model for open-channel flows

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