scholarly journals Parallel algorithms for solving the problem of coastal bottom relief dynamics

2020 ◽  
pp. 196-206
Author(s):  
А.И. Сухинов ◽  
А.Е. Чистяков ◽  
Е.А. Проценко ◽  
В.В. Сидорякина ◽  
C.B. Проценко
Keyword(s):  
Sediment Transport ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Water Environment ◽  
Continuous Model ◽  
State Equation ◽  
Navier Stokes ◽  
Coastal Zones ◽  
Navier Stokes Equations ◽  
Bottom Deformation

Предложена нестационарная 2D-модель транспорта донных отложений в прибрежной зоне мелководных водоемов, дополненная уравнениями Навье–Стокса, неразрывности и состояния водной среды. Дискретная модель транспорта наносов получена в результате аппроксимации соответствующей линеаризованной непрерывной модели. Поскольку задачи прогнозирования транспорта наносов требуют решения в реальном или ускоренном масштабах времени, на сетках, включающих 106–109 узлов, необходима разработка параллельных алгоритмов задач гидродинамики на системах с массовым параллелизмом. Представлены результаты работы созданного эффективного программного обеспечения для выполнения гидродинамических вычислительных экспериментов, позволяющие проводить численное моделирование деформации дна в прибрежной зоне водоема. Приведены результаты численных экспериментов. A nonstationary 2D model of bottom sediment transport in the coastal zones of shallow water reservoirs is supplemented with the Navier–Stokes equations, the continuity equation, and the state equation of the water environment. A discrete model of sediment transport is obtained by approximating the corresponding linearized continuous model. Since the problems of predicting sediment transport need to be solved in real or accelerated time scales, parallel algorithms for hydrodynamic problems on systems with mass parallelism should be developed on grids with 106–109 nodes. The paper contains the results obtained by an efficient software implemented to perform hydrodynamic computational experiments that allow the numerical modeling of bottom deformation in the coastal zones of reservoir. The results of numerical experiments are discussed.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

scholarly journals Experimental study and numerical simulation of dam reservoir sediment release

Water SA ◽  
2020 ◽  
Vol 46 (4 October) ◽  
Author(s):  
Marzieh Fadaee ◽  
Mohammad Zounemat-Kermani
Keyword(s):  
Numerical Simulation ◽  
Sediment Transport ◽  
Relative Error ◽  
Water Wave ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Navier Stokes Equations ◽  
Water And Sediment ◽  
Three Phase

In this research, experimental and numerical modelling of three-phase air, water, and sediment transport flow, due to the opening of a sluice gate was conducted in two scenarios, i.e., with and without a triangular obstacle. Numerical simulation was conducted using the Navier-Stokes equations with the aid of the volume of fluid method (VOF) to track the free surface of the fluid. For the experimental model, a glass-enclosed flume with 150 × 30 × 50 cm dimensions was used. The experiment was performed for an initial height of the water column at 20 cm and 10 cm sediment column. To evaluate the numerical model's performance, the simulation results were compared with the experimental observations using the average relative error %. The amount of relative error between experimental observations and numerical simulations, for the position and height of the wave flow for the three-phase air, water, and sediment flow, were obtained as 2.64% and 4.51% for the position and height of the water wave, and 2.23% and 2.82% for the position and height of the sediment transport, respectively, for the ‘without obstacle’ scenario, and 3.77% and 5.25% for the position and height of the water wave, and 2% and 7.23% for the position and height of the sediment transport, respectively, for the ‘with obstacle’ scenario. The findings of the study indicate the appropriate performance of the numerical model in the simulation of water and sediment wavefront advance, and also its weakness in the estimation of wave height.

Analysis and Methods in Fluid Mechanics

1991 ◽  
Vol 02 (01) ◽  
pp. 75-85
Author(s):  
BERTIL GUSTAFSSON
Keyword(s):  
Numerical Methods ◽  
Stokes Equations ◽  
Continuous Model ◽  
Finite Volume Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Structured Grid ◽  
Overlapping Grids ◽  
Artificial Boundaries ◽  
Stability And Accuracy

When constructing numerical methods for partial differential equations, it is important to have a thorough understanding of the continuous model and the characteristic properties of its solutions. We shall present methods of analysis for determining well-posedness of hyperbolic and mixed hyperbolic-parabolic équations which are applicable to the time-dependent Euler and Navier-Stokes equations. We shall then discuss difference- and finite volume methods and the construction of grids. The geometry of realistic problems is usually such that it is almost impossible to construct one structured grid. One way to overcome this difficulty is to use overlapping grids, where each domain has a structured grid. We discuss stability and accuracy of difference methods applied on such grids. Many problems in physics and engineering are defined in boundary domains, and artificial boundaries are introduced for computational reasons. In some cases one can construct accurate boundary conditions at these open boundaries. We shall indicate how this can be achieved, but we will also point out certain cases where accurate solutions are impossible to be obtained on limited domains. Finally some comments will be given on the difficulties arising when almost incompressible flow is computed. This corresponds to small Mach-numbers, and extra care must be taken when designing numerical methods. The theory will be complemented by numerical experiments for various flow problems in two space dimensions.

Numerical Investigation of Sediment Transport of Sandy Beaches by a Tsunami-Like Solitary Wave Based on Navier–Stokes Equations

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Cheng Liu ◽  
Xiaojian Liu ◽  
Changbo Jiang ◽  
Yong He ◽  
Bin Deng ◽  
...  
Keyword(s):  
Sediment Transport ◽  
Numerical Model ◽  
Solitary Wave ◽  
Stokes Equations ◽  
Laboratory Data ◽  
Sandy Beaches ◽  
Transport Processes ◽  
Navier Stokes ◽  
Wave Runup ◽  
Navier Stokes Equations

To improve our current understanding of tsunami-like solitary waves interacting with sandy beach, a nonlinear three-dimensional numerical model based on the computational fluid dynamics (CFD) tool OpenFOAM® is first self-developed to better describe the wave propagation, sediment transport, and the morphological responses of seabed during wave runup and drawdown. The finite volume method (FVM) is employed to discretize the governing equations of Navier–Stokes equations, combining with an improved volume of fluid (VOF) method to track the free surface and a k–ε model to resolve the turbulence. The computational capability of the hydrodynamics and the sediment transport module is well calibrated by laboratory data from different published references. The results verify that the present numerical model can satisfactorily reproduce the flow characteristics, and sediment transport processes under a tsunami-like solitary wave. The water-sediment transport module is then applied to investigate the effects of prominent factors, such as wave height, water depth, and beach slope, in affecting the beach profile change. Finally, a dimensionless empirical equation is proposed to describe the transport volume of onshore sediment based on simulation results, and some proper parameters are recommended through the regression. The results can be significantly helpful to evaluate the process of transported sediment by a tsunami event.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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