scholarly journals WAVETRISK-2.1: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Nicholas Keville-Reynolds Kevlahan ◽  
Florian Lemarié
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Mesh Adaptivity ◽  
Time Step ◽  
Vertical Coordinate ◽  
Slip Boundary ◽  
Modelling Framework ◽  
Atmosphere Model

Abstract. This paper introduces WAVETRISK-2.1 (i.e. WAVETRISK-OCEAN), an incompressible version of the atmosphere model wavetrisk-1.x with free-surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses DYNANICO's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic--baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth-system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.

WAVETRISK-OCEAN: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Kevlahan Nicholas
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Time Step ◽  
Vertical Coordinate ◽  
Modelling Framework ◽  
Standard Set ◽  
Atmosphere Model ◽  
Multilayer Shallow Water Equations

<p>This talk introduces WAVETRISK-OCEAN, an incompressible version of the atmosphere model WAVETRISK.  This new model is built on the same wavelet-based dynamically adaptive core as WAVETRISK, which itself uses DYNAMICO's mimetic vector-invariant multilayer shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping.  The ocean variant solves the incompressible multilayer shallow water equations with a Ripa type thermodynamic treatment of horizontal density gradients.  Time integration uses barotropic-baroclinic mode splitting via an implicit free surface formulation, which is about 15 times faster than explicit time stepping.  The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization.  Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount,  upwelling and baroclinic jet) as well as  turbulent wind-driven gyre flow in simplified geometries.  An innovative feature of WAVETRISK-OCEAN is that it could be coupled easily to the WAVETRISK atmosphere model, providing a simple integrated Earth system model using a consistent modelling framework.</p>

scholarly journals WAVETRISK-1.0: an adaptive wavelet hydrostatic dynamical core

2019 ◽  
Author(s):  
Nicholas K.-R. Kevlahan ◽  
Thomas Dubos
Keyword(s):  
Shallow Water ◽  
General Circulation ◽  
Wave Train ◽  
Shallow Water Equation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Time Step ◽  
Adaptive Wavelet ◽  
Dynamical Core ◽  
Vertical Coordinate

Abstract. This paper presents the new adaptive dynamical core wavetrisk. The fundamental features of the wavelet-based adaptivity were developed for the shallow water equation on the β-plane in Dubos and Kevlahan (2013) and extended to the icosahedral grid on the sphere in Aechtner et al. (2015). The three-dimensional dynamical core solves the compressible hydrostatic multilayer rotating shallow water equations on a multiscale dynamically adapted grid. The equations are discretized using a Lagrangian vertical coordinate version of dynamico introduced in Dubos et al. (2015). The horizontal computational grid is adapted at each time step to ensure a user-specified relative error in either the tendencies or the solution. The Lagrangian vertical grid is remapped using an adaptive Lagrangian-Eulerian (ALE) algorithm onto the initial hybrid σ pressure-based coordinates as necessary. The resulting grid is adapted horizontally, but uniform over all vertical layers. Thus, the three-dimensional grid is a set of columns of varying sizes. The code is parallelized by domain decomposition using mpi and the variables are stored in a hybrid data structure of dyadic quad trees and patches. A low storage explicit fourth order Runge-Kutta scheme is used for time integration. Validation results are presented for three standard dynamical core test cases: mountain-induced Rossby wave train, baroclinic instability of a jet stream and the Held and Suarez simplified general circulation model. The results confirm good strong parallel scaling and demonstrate that wavetrisk can achieve grid compression ratios of several hundred times compared with an equivalent static grid model.

A large time step Godunov scheme for free-surface shallow water equations

2014 ◽  
Vol 59 (21) ◽  
pp. 2534-2540 ◽  
Author(s):  
Renyi Xu ◽  
Deyu Zhong ◽  
Baosheng Wu ◽  
Xudong Fu ◽  
Runze Miao
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Time ◽  
Godunov Scheme ◽  
Time Step ◽  
Large Time Step

scholarly journals A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

2016 ◽  
Vol 7 (3) ◽  
pp. 165-190 ◽  
Author(s):  
Giovanni Tumolo
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Momentum Equation ◽  
Implicit Time ◽  
Time Step ◽  
Mesh Distortion ◽  
Structured Meshes ◽  
Conservative Discretization

Abstract As an extension of a previous work considering a fully advective formulation on Cartesian meshes, a mass conservative discretization approach is presented here for the shallow water equations, based on discontinuous finite elements on general structured meshes of quadrilaterals. A semi-implicit time integration is performed by employing the TR-BDF2 scheme and is combined with the semi-Lagrangian technique for the momentum equation only. Indeed, in order to simplify the derivation of the discrete linear Helmoltz equation to be solved at each time-step, a non-conservative formulation of the momentum equation is employed. The Eulerian flux form is considered instead for the continuity equation in order to ensure mass conservation. Numerical results show that on distorted meshes and for relatively high polynomial degrees, the proposed numerical method fully conserves mass and presents a higher level of accuracy than a standard off-centered Crank Nicolson approach. This is achieved without any significant imprinting of the mesh distortion on the solution.

EARLY EXPERIENCES WITH THE 360TF IBM BLUE GENE/L PLATFORM

2008 ◽  
Vol 05 (02) ◽  
pp. 237-253 ◽  
Author(s):  
G. BHANOT ◽  
J. M. DENNIS ◽  
J. EDWARDS ◽  
W. GRABOWSKI ◽  
M. GUPTA ◽  
...  
Keyword(s):  
Test Problem ◽  
Time Integration ◽  
Atmospheric Model ◽  
Horizontal Resolution ◽  
Implicit Time ◽  
Preconditioned Conjugate Gradient ◽  
Time Step ◽  
Climate System Model ◽  
Vertical Coordinate ◽  
Blue Gene

The High Order Method Modeling Environment is a scalable, spectral-element-based prototype for the Community Atmospheric Model component of the Community Climate System Model. The 3D moist primitive equations are solved on the cubed sphere with a hybrid pressure η vertical coordinate using an Emanuel convective parametrization for moist processes. Semi-implicit time integration, based on a preconditioned conjugate gradient solver, circumvents the time step restrictions associated with gravity waves. Benchmarks for two standard tests problems at 10 km horizontal resolution have been run on Blue Gene/L. Results obtained on a 32-rack Blue Gene/L system (65,536 processors, 183.5-teraflop peak) show sustained performance of 8.0 teraflops on 32,768 processors for the moist Held–Suarez test problem in coprocessor mode and 11.3 teraflops on 32,768 processors for the aquaplanet test problem, running in virtual node mode.

A Two-Stage Fourth-Order Multimoment Global Shallow-Water Model on the Cubed Sphere

2020 ◽  
Vol 148 (10) ◽  
pp. 4267-4279
Author(s):  
Yuzhang Che ◽  
Chungang Chen ◽  
Feng Xiao ◽  
Xingliang Li ◽  
Xueshun Shen
Keyword(s):  
Shallow Water ◽  
Fourth Order ◽  
Time Integration ◽  
Water Model ◽  
Shallow Water Model ◽  
Time Step ◽  
Two Stage ◽  
Order Scheme ◽  
Runge Kutta ◽  
Cubed Sphere

AbstractA new multimoment global shallow-water model on the cubed sphere is proposed by adopting a two-stage fourth-order Runge–Kutta time integration. Through calculating the values of predicted variables at half time step t = tn + (1/2)Δt by a second-order formulation, a fourth-order scheme can be derived using only two stages within one time step. This time integration method is implemented in our multimoment global shallow-water model to build and validate a new and more efficient numerical integration framework for dynamical cores. As the key task, the numerical formulation for evaluating the derivatives in time has been developed through the Cauchy–Kowalewski procedure and the spatial discretization of the multimoment finite-volume method, which ensures fourth-order accuracy in both time and space. Several major benchmark tests are used to verify the proposed numerical framework in comparison with the existing four-stage fourth-order Runge–Kutta method, which is based on the method of lines framework. The two-stage fourth-order scheme saves about 30% of the computational cost in comparison with the four-stage Runge–Kutta scheme for global advection and shallow-water models. The proposed two-stage fourth-order framework offers a new option to develop high-performance time marching strategy of practical significance in dynamical cores for atmospheric and oceanic models.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

Scalability studies and large grid computations for surface combatant using CFDShip-Iowa

2011 ◽  
Vol 25 (4) ◽  
pp. 466-487 ◽  
Author(s):  
Shanti Bhushan ◽  
Pablo Carrica ◽  
Jianming Yang ◽  
Frederick Stern
Keyword(s):  
Free Surface ◽  
Message Passing Interface ◽  
Free Surface Flows ◽  
Processing Unit ◽  
Mean Flow ◽  
Time Step ◽  
Vortical Structures ◽  
Cpu Time ◽  
Surface Combatant ◽  
Straight Ahead

Scalability studies and computations using the largest grids to date for free-surface flows are performed using message-passing interface (MPI)-based CFDShip-Iowa toolbox curvilinear (V4) and Cartesian (V6) grid solvers on Navy high-performance computing systems. Both solvers show good strong scalability up to 2048 processors, with V6 showing somewhat better performance than V4. V6 also outperforms V4 in terms of the memory requirements and central processing unit (CPU) time per time-step per grid point. The explicit solvers show better scalability than the implicit solvers, but the latter allows larger time-step sizes, resulting in a lower total CPU time. The multi-grid HYPRE solver shows better scalability than the portable, extensible toolkit for scientific computation solver. The main scalability bottleneck is identified to be the pressure Poisson solver. The memory bandwidth test suggests that further scalability improvements could be obtained by using hybrid MPI/open multi-processing (OpenMP) parallelization. V4-detached eddy simulation (DES) on a 300 M grid for the surface combatant model DTMB 5415 in the straight-ahead condition provides a plausible description of the vortical structures and mean flow patterns observed in the experiments. However, the vortex strengths are over predicted and the turbulence is not resolved. V4-DESs on up to 250 M grids for DTMB 5415 at 20° static drift angle significantly improve the forces and moment predictions compared to the coarse grid unsteady Reynolds averaged Navier–Stokes, due to the improved resolved turbulence predictions. The simulations provide detailed resolution of the free-surface and breaking pattern and vortical and turbulent structures, which will guide planned experiments. V6 simulations on up to 276 M grids for DTMB 5415 in the straight-ahead condition predict diffused vortical structures due to poor wall-layer predictions. This could be due to the limitations of the wall-function implementation for the immersed boundary method.

Sign in / Sign up

Export Citation Format

Share Document