scholarly journals A Prediction–Correction Solver for Real-Time Simulation of Free-Surface Flows in River Networks

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2525 ◽  
Author(s):  
Dechao Hu ◽  
Chengwei Lu ◽  
Shiming Yao ◽  
Shuai Yuan ◽  
Yonghui Zhu ◽  
...  
Keyword(s):  
Free Surface ◽  
River System ◽  
Free Surface Flows ◽  
River Network ◽  
Water Levels ◽  
River Networks ◽  
Time Step ◽  
Flow Process ◽  
Surface Flows ◽  
Pcm Model

A prediction–correction solver is presented here for rapid simulation of free-surface flows in dendritic and looped river networks. Rather than solving a large global algebraic system over the entire domain of river networks, the model solves subsystems for subdomains of branches in two steps: prediction and correction. With the help of the prediction–correction method (PCM), the partial linearization technique, the semi-implicit method, and the Eulerian–Lagrangian method (ELM), the model only needs to solve tridiagonal linear systems for branches and is free of any iteration. The new model was tested using a hypothetical looped river network with regular cross sections, the Three Gorges Reservoir (TGR) dendritic river network, and the Jing-south looped river system (with seasonally flooding branches). In the first test, a time-step sensitivity study was conducted and the model was revealed to produce accurate simulations at large time steps when the condition for application of the PCM to river networks was satisfied. In the TGR test, the PCM model provided almost the same histories of water levels and discharges as those simulated by the HEC-RAS model. In the Jing-south test, the mean absolute error in simulated water levels was 0.07–0.24 m, and the relative error in simulated cross-section water flux was 0.5–4.9% compared with field data; the conservation error was generally 2 × 10−4 to 3 × 10−4. The PCM model was revealed to be 2–4 times as fast as a reported model, which solves local nonlinear subsystems using two-layer iterations, and 1.2–1.4 times as fast as the HEC-RAS. Using a time step of 1200 s, it took the sequential code 26.8 and 23.1 s to complete a simulation of a one-year unsteady flow process, respectively, in the TGR river networks (with 588 cells) and the Jing-south river system (with 662 cells).

Numerical Simulation of Transient Free Surface Flows Using a Moving Mesh Technique

2006 ◽  
Vol 73 (6) ◽  
pp. 1017-1025 ◽  
Author(s):  
Laura Battaglia ◽  
Jorge D’Elía ◽  
Mario Storti ◽  
Norberto Nigro
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Surface Flows ◽  
Flow Domain ◽  
Convection Dominated

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, “A Multidimensional Upwind Scheme With no Crosswind Diffusion,” in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19–35, and Brooks, A. N., and Hughes, T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, “Stablized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, “Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,” Comput. Methods Appl. Mech. Eng., 95, pp. 221–242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented.

scholarly journals A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

2020 ◽  
Author(s):  
Matteo Bergami ◽  
Walter Boscheri ◽  
Giacomo Dimarco
Keyword(s):  
Free Surface ◽  
Sediment Transport ◽  
Numerical Scheme ◽  
Control Volume ◽  
Free Surface Flows ◽  
High Order ◽  
Time Step ◽  
Reconstruction Procedure ◽  
Surface Flows ◽  
Lagrangian Scheme

AbstractIn this paper, we present a conservative semi-Lagrangian scheme designed for the numerical solution of 3D hydrostatic free surface flows involving sediment transport on unstructured Voronoi meshes. A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume. This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms. The presented method is fully conservative by construction, since the transported quantity or the vector field is integrated for each cell over the deformed volume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element. The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations. Furthermore, a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance, hence yielding a stability condition which depends only on the explicit discretization of the viscous terms. A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment, which is assumed to be passive. The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solution whenever is known. The new numerical scheme can reach up to fourth order of accuracy on general orthogonal meshes composed by Voronoi polygons.

scholarly journals Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows

2021 ◽  
Author(s):  
Niklas Kühl ◽  
Michael Hinze ◽  
Thomas Rung
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Bubble Formation ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Steady Flows ◽  
Two Phase Flows ◽  
Time Step ◽  
Two Phase ◽  
Surface Flows

AbstractThe paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive contribution derived from a Cahn-Hilliard (CH) model and its benefits for simulating immiscible, incompressible two-phase flows. Such flows are predominantly simulated with implicit VoF schemes, which mostly employ heuristic downwind-biased approximations for the concentration transport to mimic a sharp interface. This strategy introduces a severe time step restriction and requires pseudo time-stepping of steady flows. Our overall goal is a sound description of the free-surface region that alleviates artificial time-step restrictions, supports an efficient and robust upwind-based approximation framework, and inherently includes surface tension effects when needed. The Cahn-Hilliard Navier-Stokes (CH-NS) system is verified for an analytical Couette-flow example and the bubble formation under the influence of surface tension forces. 2D validation examples are concerned with laminar standing waves reaching from gravity to capillary scale as well as a submerged hydrofoil flow. The final application refers to the 3D flow around an experimentally investigated container vessel at fixed floatation for Re = 1.4 × 107 and Fn = 0.26. Results are compared with data obtained from VoF approaches, supplemented by analytical solutions and measurements. The study indicates the superior efficiency, resharpening capability, and wider predictive realm of the CH-based extension for free-surface flows with a confined spatial range of interface Courant numbers.

A Splitting Method for Numerical Simulation of Free Surface Flows of Incompressible Fluids with Surface Tension

2015 ◽  
Vol 15 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Kirill D. Nikitin ◽  
Maxim A. Olshanskii ◽  
Kirill M. Terekhov ◽  
Yuri V. Vassilevski
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Stability Result ◽  
Free Surface Flows ◽  
Fluid Inertia ◽  
Time Step ◽  
Surface Flows ◽  
Level Set Function

AbstractThe paper studies a splitting method for the numerical time-integration of the system of partial differential equations describing the motion of viscous incompressible fluid with free boundary subject to surface tension forces. The method splits one time step into a semi-Lagrangian treatment of the surface advection and fluid inertia, an implicit update of viscous terms and the projection of velocity into the subspace of divergence-free functions. We derive several conservation properties of the method and a suitable energy estimate for numerical solutions. Under certain assumptions on the smoothness of the free surface and its evolution, this leads to a stability result for the numerical method. Efficient computations of free surface flows of incompressible viscous fluids need several other ingredients, such as dynamically adapted meshes, surface reconstruction and level set function re-initialization. These enabling techniques are discussed in the paper as well. The properties of the method are illustrated with a few numerical examples. These examples include analytical tests and the oscillating droplet benchmark problem.

scholarly journals Fast and high-precision simulation of hydrodynamic and water quality process in river networks

2018 ◽  
Vol 246 ◽  
pp. 01073
Author(s):  
Chengwei Lu ◽  
Jianzhong Zhou ◽  
Dechao Hu ◽  
Shuai Yuan ◽  
Yi Liu
Keyword(s):  
Water Quality ◽  
Free Surface ◽  
High Precision ◽  
Hydrodynamic Model ◽  
Free Surface Flows ◽  
Computational Time ◽  
River Networks ◽  
Time Step ◽  
Advection Term ◽  
Quality Process

To realize a fast and high-precision simulation of unsteady flows and water quality process in river networks, a 1-D mathematical modelling system for free-surface flows and water quality process is developed. In the hydrodynamic model, a θ semi-implicit method is used to discretize the free-surface gradient term in the momentum equation while the Eulerian-Lagrangian method is employed to solve the advection term. To achieve good mass conservation, the finite-volume method is used to discretize continuity equation. Moreover, the resulting hydrodynamic model is unconditionally stable with respect to the gravity wave speed and flow advection. In solving the scalar transport equation, the forward difference is used for discretization in time while the centre-difference is in space. A sub-cycling is introduced to divide the computational time step and improve the stability of water quality model. Therefore, large time steps are allowed in both the hydrodynamic and the transport models. The coupling of the branches of the river networks is solved using a predictioncorrection method. Then, a Gaussian pulse test and a rectangular wave test are employed to demonstrate the accuracy and the efficiency of the system, which will also provide powerful supports for ecological operations of cascade reservoirs in drainage basins.

scholarly journals Viscous free-surface flows past cylinders

2020 ◽  
Vol 5 (8) ◽  
Author(s):  
Edward M. Hinton ◽  
Andrew J. Hogg ◽  
Herbert E. Huppert
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Surface Flows
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