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Runge–Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Hilary Weller, Sarah-Jane Lock, Nigel Wood
2013 Journal of Computational Physics  
We demonstrate how a number of Runge-Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI.  ...  The stability limits of a number of variations of trapezoidal implicit and some Runge-Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq  ...  We would also like to thank Thomas Allen (Met Office) for useful input to this work.  ... 
doi:10.1016/j.jcp.2013.06.025 fatcat:jdwm6n33yredddywlsqcoiqzim

Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models

David J. Gardner, Jorge E. Guerra, François P. Hamon, Daniel R. Reynolds, Paul A. Ullrich, Carol S. Woodward
2018 Geoscientific Model Development  
The IMEX formulations considered include horizontally explicitvertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly.  ...  In this work, we investigate various implicit–explicit (IMEX) additive RungeKutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric  ...  Horizontally explicit vertically implicit splittings In this section we present four horizontally explicit vertically implicit (HEVI) formulations of the non-hydrostatic equations (1) 5 -(5) in which the  ... 
doi:10.5194/gmd-11-1497-2018 fatcat:a7nmjjjwwjbppnhbqmntar3xwm

Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models

David J. Gardner, Jorge E. Guerra, François P. Hamon, Daniel R. Reynolds, Paul A. Ullrich, Carol S. Woodward
2017 Geoscientific Model Development Discussions  
In this work we investigate various implicit-explicit (IMEX) additive Runge-Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric  ...  The IMEX formulations considered include horizontally implicit-vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly.  ...  The version of Tempest that includes ARKode interfaces used for this work and splittings with horizontally implicit terms is available in the Git repository at https://github.com/gardner48/tempestmodel  ... 
doi:10.5194/gmd-2017-285 fatcat:zk53fuvepbfldn5hwg5lokzz4m

Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

Gianmarco Mengaldo, Andrzej Wyszogrodzki, Michail Diamantakis, Sarah-Jane Lock, Francis X. Giraldo, Nils P. Wedi
2018 Archives of Computational Methods in Engineering  
the main drivers in terms of cost-to-solution (e.g., time-or energy-to-solution), accuracy and numerical stability, thus constituting one of the key building blocks of the computational model.  ...  In addition, the potential for the co-design of time-stepping algorithms and underlying high performance computing hardware, a keystone to accelerate the computational performance of future NWP and climate  ...  FXG gratefully acknowledges the support of the U.S. Office  ... 
doi:10.1007/s11831-018-9261-8 fatcat:mj7vbyhttjd7lid7xwrgztdayu

Acceleration of the Implicit-Explicit Non-hydrostatic Unified Model of the Atmosphere (NUMA) on Manycore Processors [article]

Daniel S. Abdi, Francis X. Giraldo, Emil M. Constantinescu, Lester E. Carr III, Lucas C. Wilcox, Timothy C. Warburton
2017 arXiv   pre-print
complement; b) formulating a horizontally-explicit vertically-implicit (HEVI) 1D-IMEX scheme that has a lower workload and potentially better scalability than 3D-IMEX; c) using high-order polynomial preconditioners  ...  to reduce the condition number of the resulting system; d) using a direct solver for the 1D-IMEX method by performing and storing LU factorizations once to obtain a constant cost for any Courant number  ...  The strong scalability of IMEX on a multi-GPU cluster is evaluated using larger grid resolutions of 13 km, 10 km and 3km achieved using 6x112x112x4, 6x144x144x4 and 6x448x448x4 elements, respectively,  ... 
arXiv:1702.04316v1 fatcat:ggnav5pbkrg4xppdiczv3ofuwm

A framework to evaluate IMEX schemes for atmospheric models

Oksana Guba, Mark A. Taylor, Andrew M. Bradley, Peter A. Bosler, Andrew Steyer
2020 Geoscientific Model Development  
We present a new evaluation framework for implicit and explicit (IMEX) RungeKutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes.  ...  We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX RungeKutta methods with a high Courant–Friedrichs–Lewy (CFL) number.  ...  The authors thank an anonymous reviewer and Financial support. This research has been supported by the US DOE, Office of Science. Review statement.  ... 
doi:10.5194/gmd-13-6467-2020 fatcat:wevsfs37yzd4xnkbebo5pskhom

Exploring the Effects of a High-order Vertical Coordinate in a Non-hydrostatic Global Model

Paul A. Ullrich, Jorge E. Guerra
2015 Procedia Computer Science  
The SNFEM formulation generalizes traditional second-order vertical discretizations, including Lorenz and Charney-Phillips discretizations, to arbitrary order-of-accuracy while preserving desirable properties  ...  As atmospheric models are pushed towards non-hydrostatic resolutions, there is a growing need for new numerical discretizations that are accurate, robust and effective at these scales.  ...  in the vertical (a technique known as Horizontally Explicit Vertically Implicit, HEVI).  ... 
doi:10.1016/j.procs.2015.05.475 fatcat:b32kv4fyfbbnrptpyd6fl25tbq

IMEX and Semi-Implicit Runge-Kutta Schemes for CFD Simulations [article]

Arman Rokhzadi, University, My, University, My
2018
Therefore, a comprehensive effort has been made toward minimizing the numerical errors to develop new Runge-Kutta schemes, in IMEX and semi-implicit forms, to temporally integrate the governing equations  ...  In the combined method, the linear part of the equation as well as the fast wave terms are treated by the implicit part and the rest is calculated by the explicit scheme.  ...  Acknowledgment The authors wish to acknowledge financial support from Natural Sciences and Engineering Research Council of Canada (NSERC).  ... 
doi:10.20381/ruor-22215 fatcat:vwol2erbwfhrtkdbqnaoxnj6su

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Simone Marras, James F. Kelly, Margarida Moragues, Andreas Müller, Michal A. Kopera, Mariano Vázquez, Francis X. Giraldo, Guillaume Houzeaux, Oriol Jorba
2015 Archives of Computational Methods in Engineering  
One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (2003) [Review of numerical methods for nonhydrostatic weather prediction models Meteorol. Atmos.  ...  As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where  ...  More recent work on IMEX methods includes [87] , which utilizes Adams and backward di erence methods, and [314] , which takes a horizontally-explicit vertically-implicit (HEVI) approach.  ... 
doi:10.1007/s11831-015-9152-1 fatcat:tmjzwcxorfgt5fdcrlf6kb24ny

A two-stage fourth-order multi-moment global shallow water model on cubed sphere

Yuzhang Che, Chungang Chen, Feng Xiao, Xingliang Li, Xueshun Shen
2020 Monthly Weather Review  
The two-stage fourth-order scheme saves about 30% computational cost in comparison with the four-stage Runge-Kutta scheme for global advection and shallow water models.  ...  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  ...  This work is supported by The National Key Research and Development  ... 
doi:10.1175/mwr-d-20-0004.1 fatcat:kw6txg5iezfazkpx3vlvo5ciim

High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations [article]

Rihui Lan, Lili Ju, Zhu Wang, Max Gunzburger, Philip Jones
2021 arXiv   pre-print
Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in  ...  In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling  ...  Wood, RungeKutta IMEX schemes for the horizontally ex- plicit/vertically implicit (HEVI) solution of wave equations, Journal of Computational Physics 252 (2013) 365–381. [43] A.  ... 
arXiv:2105.13484v2 fatcat:6tydjr6oxrav3d3oadqepvtdca

Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method [article]

Andreas Dedner, Robert Klöfkorn
2021 arXiv   pre-print
of non linear partial differential equations (PDE).  ...  This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range  ...  In some applications other types of splitting (e.g. horizontal explicit vertical implicit (HEVI) methods used in meteorology) are of interest and will be made available in future releases.  ... 
arXiv:2009.13416v2 fatcat:uzzbg2acvjehnmsyi3j7jbsvem

The ESCAPE project: Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

Andreas Müller, Willem Deconinck, Christian Kühnlein, Gianmarco Mengaldo, Michael Lange, Nils Wedi, Peter Bauer, Piotr K. Smolarkiewicz, Michail Diamantakis, Sarah-Jane Lock, Mats Hamrud, Sami Saarinen (+47 others)
2019 Geoscientific Model Development Discussions  
time-to-solution and energy-to-solution yet without compromising the accuracy and stability of the calculation.  ...  These algorithms should (i) minimise the energy footprint along with the time required to produce a solution, (ii) maintain a satisfying level of accuracy, (iii) be numerically stable and resilient, in  ...  At some point in the future we expect to reach resolutions 5 at which we will need to use Eulerian-based time-integration (EBTI), like for example horizontally explicit vertically implicit (HEVI) schemes  ... 
doi:10.5194/gmd-2018-304 fatcat:maw4jjflbbhlvd5j4mnuv36wgy

Large-eddy simulations with ClimateMachine: a new open-source code for atmospheric simulations on GPUs and CPUs [article]

Akshay Sridhar, Yassine Tissaoui, Simone Marras, Zhaoyi Shen, Charles Kawczynski, Simon Byrne, Kiran Pamnany, Maciej Waruszewski, Thomas H. Gibson, Jeremy E. Kozdon, Valentin Churavy, Lucas C. Wilcox (+2 others)
2021 arXiv   pre-print
They demonstrate the utility of ClimateMachine as a modelling tool for limited-area LES flow configurations.  ...  governing equations.  ...  We thank the Google team for their assistance with operations on the Google Cloud Platform.  ... 
arXiv:2110.00853v1 fatcat:t5jo4t4fdjg3fif5u5pe555a6m

An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus

V. Gopinath, A. Fournier, T. Gastine
2022
The ensemble comprises 28 members: 4 implicit-explicit multistep schemes, 22 implicit-explicit Runge-Kutta (IMEX-RK) schemes, and 2 fully explicit schemes used for reference.  ...  The schemes are assessed for 11 different physical setups that cover laminar and turbulent regimes.  ...  This work was made possible by support from Indo-French Centre for the Promotion of Advanced Research CEFIPRA/IFCPAR (project 5307-1).  ... 
doi:10.48550/arxiv.2202.05734 fatcat:n5jzazcs2ffr3jphdm2wl6te5i