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Moving mesh version of wave propagation algorithm based on augmented Riemann solver

APPLIED MATHEMATICS AND COMPUTATION 2020年 375卷

作者： Bagherpoorfard, Mina Soheili, Ali R. Islamic Azad Univ Dept Math Fasa Branch Fasa Iran Ferdowsi Univ Mashhad Dept Appl Math Mashhad Razavi Khorasan Iran Ctr Excellence Modelling & Control Syst Mashhad Razavi Khorasan Iran

Shallow water equations are a nonlinear system of hyperbolic conservation laws. This system admits discontinuous solutions. In addition, a discontinuous bathymetry can lead to the discontinuous solutions. The accuracy of numerical methods depends on the accuracy of the numerical solutions around these discontinuities. In order to increase the accuracy, the adaptive mesh methods are more cost-effective than the methods based on the global refinement, In terms of computational cost. Moving mesh method is an adaptive mesh method. In this method, an increase of the number of mesh points is not needed for increasing the accuracy and efficiency of numerical solutions. Highly accurate solutions only can be obtained by concentrating points in areas where more accuracy is needed and decreasing the number of points in smooth areas. In this paper, LeVeque wave propagation algorithm is improved by the moving mesh method, for shallow water equations with variable bathymetry. Moreover, augmented Riemann solver is used for solving Riemann problems in each time step. Finally, moving mesh version of wave propagation algorithm based on augmented Riemann solver is proposed. The numerical solutions based on the moving mesh method and fixed mesh method have a significant difference and application of a moving mesh method yields highly accurate solutions around shocks and discontinuities. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Finite volume methods Moving mesh methods Riemann solvers Shallow water equations wave propagation algorithm

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A fully-coupled bedload sediment transport model based on a two-dimensional modified wave propagation algorithm

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JOURNAL OF HYDRAULIC RESEARCH 2020年第2期58卷 187-203页

作者： Mahdizadeh, Hossein Sharifi, Soroosh Univ Birjand Dept Civil Engn Birjand Iran Univ Birmingham Dept Civil Engn Birmingham W Midlands England

In this paper, an extension of a second-order Godunov-type wave propagation algorithm is presented for modelling two-dimensional morphodynamic problems using a coupled approach. In this solution, the two-dimensional shallow water equations (SWEs) and bedload sediment mass balance laws are expressed in a coupled form. The proposed numerical solver treats the source term including the bedload variations as well as the friction terms within the flux-differencing of the finite-volume neighbouring cells. In order to solve the morphodynamic system in two-dimensions, the dimensional-splitting method is utilized. To consider the bedload sediment discharge within the Exner equation, the Smart and Meyer-Peter & Muller formulae are adopted. To verify the capability of the extended wave propagation solver in dealing with different flow regimes several numerical test cases are investigated. The numerical results show that for all examined cases, excellent agreement is achieved between the numerical results and the exact solutions and experimental data, confirming the effectiveness of the method.

关键词： Bedload sediment transport coupled solution flux-wave approach wave propagation algorithm

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A Third-Order Accurate wave propagation algorithm for Hyperbolic Partial Differential Equations

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Communications on Applied Mathematics and Computation 2020年第3期2卷 403-427页

作者： Christiane Helzel Institute of Mathematics Heinrich-Heine-University DüsseldorfDüsseldorfGermany

We extend LeVeque's wave propagation algorithm,a widely used finite volume method for hyperbolic partial differential equations,to a third-order accurate *** resulting scheme shares main properties with the original method,i.e.,it is based on a wave decomposition at grid cell interfaces,it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of a wave limiter.

关键词： wave propagation algorithm Hyperbolic partial differential equations Third-order accuracy

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A wave propagation algorithm for nonlinear site response analysis of layered soil accounting for liquefaction

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SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 2021年 149卷

作者： Anthi, M. Gerolymos, N. Natl Tech Univ Athens Athens Greece

A constitutive model is developed for the ground response analysis of layered sites. The model is a onedimensional version of Ta-Ger (2016) and involves critical state compatibility, anisotropic plastic flow rule and Bouc-Wen type hardening law. After being downgraded to the p-q stress space the model is reformulated to provide a unified framework of analysis for both drained and undrained loading conditions and for sand and clay. The calibration of the model parameters for sand is based on a procedure that targets to the optimum performance in both drained and undrained load conditions by simultaneously matching the response in terms of: (a) the cyclic resistance ratio curves as per the NCEER/NSF methodology, and (b) widely-used experimental shear modulus and damping ratio curves available in the literature. For the clay-like soil the calibration involves only the second step under the assumption of fully undrained conditions. The model is implemented through an explicit finite difference algorithm into an in-house computer code which performs integration of the wave equations to obtain the non-linear response of the soil. The accuracy of the algorithm is verified through comparison with analytical solutions for the amplification function of soil deposits with linearly increasing Vs, subjected to vertically propagating shear waves. It is then validated against experimental data from two centrifuge experiments. Finally, the records of the Port Island array from Kobe 1995 earthquake are employed to test the ability of the model to predict the observed response.

关键词： wave propagation algorithm Liquefaction 1D plasticity model Cyclic loading Drained and undrained load conditions Nonlinear site response analysis Centrifuge experiments Kobe 1995 earthquake

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On the Approximation of Two-Dimensional Transient Pipe Flow Using a Modified wave propagation algorithm

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JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME 2018年第7期140卷 071402页

作者： Mahdizadeh, Hossein Sharifi, Soroosh Omidvar, Pourya Univ Birjand Dept Civil Engn Birjand 97175615 South Khorasan Iran Univ Birmingham Dept Civil Engn Sch Engn Birmingham B15 2TT W Midlands England Univ Yasuj Dept Mech Engn Daneshjoo Ave Yasuj *** Iran

In this study, a second-order accurate Godunov-type finite volume method is used for the solution of the two-dimensional (2D) water hammer problem. The numerical scheme applied here is well balanced and is able to treat the unsteady friction terms, together with the convective terms, within the differences between fluxes of neighboring computational cells. In order to consider the effect of unsteady friction terms during the water hammer process, k-epsilon and k-omega turbulence models are employed. The performance of the proposed method with the choice of different turbulence models is evaluated using experimental data obtained from one low and one high Reynolds-number turbulent test cases. In addition to velocity and pressure distributions, the turbulence characteristics of each variant of the model, including eddy viscosity, dissipation rate, and turbulent kinetic energy during the water hammer process are fully analyzed. It is found that the inclusion of the convective inertia terms leads to more accurate pressure profiles. The results also show that using a relatively high Courant-Friedrichs-Lewy (CFL) number close to unity, the introduced numerical solver with both choices of turbulence models provides reasonable and acceptable predictions for the studied flows.

关键词： flux-wave approach k-epsilon turbulence model k-omega turbulence model water hammer problem wave propagation algorithm

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A modified flux-wave formula for the solution of second-order macroscopic traffic flow models

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NONLINEAR DYNAMICS 2021年第4期106卷 3507-3520页

作者： Araghi, M. Mahdizadeh, S. Mahdizadeh, H. Moodi, S. Univ Birjand Dept Civil Engn Birjand Iran Ferdowsi Univ Mashhad Dept Civil Engn Mashhad Razavi Khorasan Iran Univ Sistan & Baluchesatn Dept Civil Engn Zahedan Iran

In this paper, a second-order Godunov-type finite volume technique based upon the wave propagation algorithm has been defined which mainly addresses second-order, one-dimensional, macroscopic traffic flow models. Four widely used models that have fundamental differences in terms of the equations form were chosen to evaluate this formula. These models use Riemann's solution propagating different jump discontinuity from each finite-volume cell interface. The proposed modified flux-wave formula is well-balanced and includes the related source term within the flux-differencing from each cell interface. Therefore, no additional numerical treatment is required with respect to the source terms. The numerical results obtained herein have been compared with high-order relaxations schemes including fifth-order WENO and second-order MUSCL (for three models in a straight homogeneous road) and Roe decomposition technique (for two models in a ring road). The results show that the defined approach is capable to provide stable and realistic response for the macroscopic traffic models without numerical diffusion. Additionally, a very good agreement achieved with the reference solution and also higher order schemes. It is also inferred that the plausibility and positivity conserving conditions have been maintained for the modified flux wave approach for all of the examined models.

关键词： Second-order macroscopic traffic flow models wave propagation algorithm Riemann solver Flux wave Numerical modelling

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Coupled and splitting bedload sediment transport models based on a modified flux-wave approach

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International Journal of Sediment Research 2021年第1期36卷 38-49页

作者： Hossein Mahdizadeh Soroosh Sharifi Department of Civil Engineering University of Birjand Department of Civil Engineering University of Birmingham

Numerical modeling of free-surface flow over a mobile bed with predominantly bedload sediment transport can be done by solving the shallow water and Exner equations using coupled and splitting *** coupled method uses a coupling of the governing equations at the same time step leading to a non-conservative *** splitting method solves the Exner and the shallow water equations in a separate manner,and is only capable of modeling weak free-surface and bedload *** the current study,an extended version of a Godunov-type wave propagation algorithm is presented for modeling of morphodynamic systems using both coupled and splitting *** the introduced coupled method the entire morphodynamic system is solved in the form of a conservation *** the splitting technique,a new wave Riemann decomposition is defined which enables the scheme to be utilized for mild and strong *** consider the bedload sediment discharge within the Exner equation,the Smart and Meyer-Peter & Miiller formulae are *** was found that the coupled solution gives accurate predictions for all investigated flow regimes including pro pagation over a dry-state using a Courant-Friedrichs-Lewy(CFL) number equal to ***,the splitting method was able to model all flow regimes with a lower CFL number of 0.3.

关键词： Bedload sediment transport Coupled solution Flux-wave method Shallow water equations Splitting technique wave propagation algorithm

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Flood wave Modeling Based on a Two-Dimensional Modified wave propagation algorithm Coupled to a Full-Pipe Network Solver

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JOURNAL OF HYDRAULIC ENGINEERING-ASCE 2012年第3期138卷 247-259页

作者： Mahdizadeh, Hossein Stansby, Peter K. Rogers, Benedict D. Univ Manchester Sch Mech Aerosp & Civil Engn Manchester M13 9PL Lancs England Univ Manchester Tyndall Ctr Climate Change Res Manchester M13 9PL Lancs England

Flood propagation over urban areas can cause an interaction between the free-surface flow and large underground pipe networks used for sewage and storm drainage, causing outflows and inflows at the bed. The waves resulting from these bed discharges may collide with each other and the surface waves, increasing water depths, velocities and accelerations, and their interaction thus affects flood risk. The authors previously introduced a one-dimensional (1D) shallow-water model for simulating free-surface interaction with the flows issuing vertically through finite gaps, referred to as efflux. This model used a modified wave propagation algorithm and was validated by comparing results with the full Navier-Stokes equation solver (STAR-CD) based on the volume-of-fluid method, which models free-surface motion quite generally, although at considerable computational expense. The present paper extends the shallow-water scheme to two dimensions, including source terms for pipe outflow/inflow (efflux/influx) and bed friction and bathymetry gradients. A general pipe network solver for full flow is coupled with the free-surface flow. The methodology is first tested with idealized cases. Two-dimensional (2D) dam-break flow over a complex bed profile without efflux/influx at the bed is first modeled. Next, efflux discharge is modeled in isolation over a dry bed and then with dam-break interaction, comparing with 3D STAR-CD results. Results for these idealized cases are in good agreement. Finally dam-break interaction with a pipe network of 25 nodes demonstrates the complex bore interaction. DOI: 10.1061/(ASCE)HY.1943-7900.0000515. (C) 2012 American Society of Civil Engineers.

关键词： Two-dimensional shallow water equations Riemann solver Pipe network solver wave propagation algorithm Navier-Stokes equations

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Shock focusing flow field simulated by a high-resolution numerical algorithm

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SHOCK waveS 2012年第6期22卷 641-645页

作者： Jung, Y. G. Chang, K. S. Korea Adv Inst Sci & Technol Sch Mech Aerosp & Syst Engn Taejon 305701 South Korea

Shock-focusing concave reflector is a very simple and effective tool to obtain a high-pressure pulse wave near the physical focal point. In the past, many optical images were obtained through experimental studies. However, measurement of field variables is not easy because the phenomenon is of short duration and the magnitude of shock waves is varied from pulse to pulse due to poor reproducibility. Using a wave propagation algorithm and the Cartesian embedded boundary method, we have successfully obtained numerical schlieren images that resemble the experimental results. By the numerical results, various field variables, such as pressure, density and vorticity, become available for the better understanding and design of shock focusing devices.

关键词： Shock focusing wave propagation algorithm Cartesian embedded boundary method Focal point

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Numerical treatment of two-dimensional interfaces for acoustic and elastic waves

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JOURNAL OF COMPUTATIONAL PHYSICS 2004年第1期195卷 90-116页

作者： Lombard, B Piraux, J Lab Mecan & Acoust F-13402 Marseille France

We present a numerical method to take into account 2D arbitrary-shaped interfaces in classical finite-difference schemes, on a uniform Cartesian grid. This work extends the "explicit simplified interface method" (ESIM), previously proposed in ID [J. Comput. Phys. 168 (2001) 227-248]. The physical problem under study concerns the linear hyperbolic systems of acoustics and elastodynamics, with stationary interfaces. Our method maintains, near the interfaces, properties of the schemes in homogeneous medium, such as the order of accuracy and the stability limit. Moreover, it enforces the numerical solution to satisfy the exact interface conditions. Lastly, it provides subcell geometrical features of the interface inside the meshing. The ESIM can be coupled automatically with a wide class of numerical schemes (Lax-Wendroff, flux-limiter schemes, etc.) for a negligible additional computational cost. Throughout the paper, we focus on the challenging case of an interface between a fluid and an elastic solid. In numerical experiments, we provide comparisons between. numerical solutions and original analytic solutions, showing the efficiency of the method. (C) 2003 Elsevier Inc. All rights reserved.

关键词： acoustics and elastodynamics discontinuous coefficients jump conditions interface methods wave propagation algorithm singular value decomposition hyperbolic systems

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