Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning
Abstract
Here, this paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step of the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1362122
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Scientific Computing
- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 1064-8275
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 54 ENVIRONMENTAL SCIENCES; Euler equations; atmospheric flows; characteristic-based splitting; compressible; implicit-explicit time integration; nonhydrostatic
Citation Formats
Ghosh, Debojyoti, and Constantinescu, Emil M. Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning. United States: N. p., 2016.
Web. doi:10.1137/15M1044369.
Ghosh, Debojyoti, & Constantinescu, Emil M. Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning. United States. https://doi.org/10.1137/15M1044369
Ghosh, Debojyoti, and Constantinescu, Emil M. Thu .
"Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning". United States. https://doi.org/10.1137/15M1044369. https://www.osti.gov/servlets/purl/1362122.
@article{osti_1362122,
title = {Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning},
author = {Ghosh, Debojyoti and Constantinescu, Emil M.},
abstractNote = {Here, this paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step of the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.},
doi = {10.1137/15M1044369},
journal = {SIAM Journal on Scientific Computing},
number = 3,
volume = 38,
place = {United States},
year = {2016},
month = {6}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Euler solutions using flux-based wave decomposition
journal, January 2007
- Ahmad, Nash'at; Lindeman, John
- International Journal for Numerical Methods in Fluids, Vol. 54, Issue 1
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
journal, November 1997
- Ascher, Uri M.; Ruuth, Steven J.; Spiteri, Raymond J.
- Applied Numerical Mathematics, Vol. 25, Issue 2-3
A Blended Soundproof-to-Compressible Numerical Model for Small- to Mesoscale Atmospheric Dynamics
journal, December 2014
- Benacchio, Tommaso; O’Neill, Warren P.; Klein, Rupert
- Monthly Weather Review, Vol. 142, Issue 12
A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows
journal, March 2000
- Bonaventura, Luca
- Journal of Computational Physics, Vol. 158, Issue 2
Well balanced finite volume methods for nearly hydrostatic flows
journal, May 2004
- Botta, N.; Klein, R.; Langenberg, S.
- Journal of Computational Physics, Vol. 196, Issue 2
A semi-implicit time-splitting scheme for a regional nonhydrostatic atmospheric model
journal, March 2012
- Bourchtein, Andrei; Bourchtein, Ludmila
- Computer Physics Communications, Vol. 183, Issue 3
Multirate Timestepping Methods for Hyperbolic Conservation Laws
journal, September 2007
- Constantinescu, Emil M.; Sandu, Adrian
- Journal of Scientific Computing, Vol. 33, Issue 3
Extrapolated Implicit-Explicit Time Stepping
journal, January 2010
- Constantinescu, Emil M.; Sandu, Adrian
- SIAM Journal on Scientific Computing, Vol. 31, Issue 6
A Non-Archimedean Approach to the Equations of Convection Dynamics
journal, November 1979
- Das, Phanindramohan
- Journal of the Atmospheric Sciences, Vol. 36, Issue 11
Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems
journal, April 2012
- Durran, Dale R.; Blossey, Peter N.
- Monthly Weather Review, Vol. 140, Issue 4
An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models
journal, May 2004
- Gassmann, A.
- Meteorology and Atmospheric Physics, Vol. 88, Issue 1-2
An anelastic allspeed projection method for gravitationally stratified flows
journal, August 2006
- Gatti-Bono, Caroline; Colella, Phillip
- Journal of Computational Physics, Vol. 216, Issue 2
Multirate linear multistep methods
journal, December 1984
- Gear, C. W.; Wells, D. R.
- BIT, Vol. 24, Issue 4
Compact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws
journal, January 2012
- Ghosh, Debojyoti; Baeder, James D.
- SIAM Journal on Scientific Computing, Vol. 34, Issue 3
Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows
journal, January 2014
- Ghosh, Debojyoti; Baeder, James D.
- Journal of Scientific Computing, Vol. 61, Issue 1
Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows
journal, April 2016
- Ghosh, Debojyoti; Constantinescu, Emil M.
- AIAA Journal, Vol. 54, Issue 4
Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms
journal, January 2015
- Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed
- SIAM Journal on Scientific Computing, Vol. 37, Issue 3
Application of Compact-Reconstruction Weighted Essentially Nonoscillatory Schemes to Compressible Aerodynamic Flows
journal, September 2014
- Ghosh, Debojyoti; Medida, Shivaji; Baeder, James D.
- AIAA Journal, Vol. 52, Issue 9
Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
journal, January 2013
- Giraldo, F. X.; Kelly, J. F.; Constantinescu, E. M.
- SIAM Journal on Scientific Computing, Vol. 35, Issue 5
A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases
journal, April 2008
- Giraldo, F. X.; Restelli, M.
- Journal of Computational Physics, Vol. 227, Issue 8
Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling
journal, January 2010
- Giraldo, F. X.; Restelli, M.; Läuter, M.
- SIAM Journal on Scientific Computing, Vol. 32, Issue 6
The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS)
journal, July 1997
- Hodur, Richard M.
- Monthly Weather Review, Vol. 125, Issue 7
A nonhydrostatic model based on a new approach
journal, January 2003
- Janjic, Z. I.
- Meteorology and Atmospheric Physics, Vol. 82, Issue 1-4
Explicit Two-Step Peer Methods for the Compressible Euler Equations
journal, July 2009
- Jebens, Stefan; Knoth, Oswald; Weiner, Rüdiger
- Monthly Weather Review, Vol. 137, Issue 7
Partially implicit peer methods for the compressible Euler equations
journal, June 2011
- Jebens, Stefan; Knoth, Oswald; Weiner, Rüdiger
- Journal of Computational Physics, Vol. 230, Issue 12
Efficient Implementation of Weighted ENO Schemes
journal, June 1996
- Jiang, Guang-Shan; Shu, Chi-Wang
- Journal of Computational Physics, Vol. 126, Issue 1
Additive Runge–Kutta schemes for convection–diffusion–reaction equations
journal, January 2003
- Kennedy, Christopher A.; Carpenter, Mark H.
- Applied Numerical Mathematics, Vol. 44, Issue 1-2
The Simulation of Three-Dimensional Convective Storm Dynamics
journal, June 1978
- Klemp, Joseph B.; Wilhelmson, Robert B.
- Journal of the Atmospheric Sciences, Vol. 35, Issue 6
A Semi-Implicit Scheme for grid Point Atmospheric Models of the Primitive Equations
journal, January 1971
- Kwizak, Michael; Robert, AndrÉ J.
- Monthly Weather Review, Vol. 99, Issue 1
Compact finite difference schemes with spectral-like resolution
journal, November 1992
- Lele, Sanjiva K.
- Journal of Computational Physics, Vol. 103, Issue 1
Weighted Essentially Non-oscillatory Schemes
journal, November 1994
- Liu, Xu-Dong; Osher, Stanley; Chan, Tony
- Journal of Computational Physics, Vol. 115, Issue 1
Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES
journal, November 2015
- Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X.
- Journal of Computational Physics, Vol. 301
An Implicitly Balanced Hurricane Model with Physics-Based Preconditioning
journal, April 2005
- Reisner, J. M.; Mousseau, A.; Wyszogrodzki, A. A.
- Monthly Weather Review, Vol. 133, Issue 4
Operator-Based Preconditioning of Stiff Hyperbolic Systems
journal, January 2010
- Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.
- SIAM Journal on Scientific Computing, Vol. 32, Issue 1
Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981
- Roe, P. L.
- Journal of Computational Physics, Vol. 43, Issue 2
The calculation of the interaction of non-stationary shock waves and obstacles
journal, January 1962
- Rusanov, V. V.
- USSR Computational Mathematics and Mathematical Physics, Vol. 1, Issue 2
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986
- Saad, Youcef; Schultz, Martin H.
- SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
Multirate Explicit Adams Methods for Time Integration of Conservation Laws
journal, August 2008
- Sandu, Adrian; Constantinescu, Emil M.
- Journal of Scientific Computing, Vol. 38, Issue 2
Conservative Scheme for the Compressible Nonhydrostatic Models with the Horizontally Explicit and Vertically Implicit Time Integration Scheme
journal, May 2002
- Satoh, Masaki
- Monthly Weather Review, Vol. 130, Issue 5
Efficiency and Accuracy of the Klemp-Wilhelmson Time-Splitting Technique
journal, November 1994
- Skamarock, William C.; Klemp, Joseph B.
- Monthly Weather Review, Vol. 122, Issue 11
A time-split nonhydrostatic atmospheric model for weather research and forecasting applications
journal, March 2008
- Skamarock, William C.; Klemp, Joseph B.
- Journal of Computational Physics, Vol. 227, Issue 7
A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics
journal, April 2014
- Smolarkiewicz, Piotr K.; Kühnlein, Christian; Wedi, Nils P.
- Journal of Computational Physics, Vol. 263
Operator-Split Runge–Kutta–Rosenbrock Methods for Nonhydrostatic Atmospheric Models
journal, April 2012
- Ullrich, Paul; Jablonowski, Christiane
- Monthly Weather Review, Vol. 140, Issue 4
Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves
journal, December 2014
- Weller, Hilary; Shahrokhi, Ava
- Monthly Weather Review, Vol. 142, Issue 12
Multirate infinitesimal step methods for atmospheric flow simulation
journal, April 2009
- Wensch, Jörg; Knoth, Oswald; Galant, Alexander
- BIT Numerical Mathematics, Vol. 49, Issue 2
A Two-Step Adams–Bashforth–Moulton Split-Explicit Integrator for Compressible Atmospheric Models
journal, October 2009
- Wicker, Louis J.
- Monthly Weather Review, Vol. 137, Issue 10
Time-Splitting Methods for Elastic Models Using Forward Time Schemes
journal, August 2002
- Wicker, Louis J.; Skamarock, William C.
- Monthly Weather Review, Vol. 130, Issue 8
The Advanced Regional Prediction System (ARPS) - A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification
journal, December 2000
- Xue, M.; Droegemeier, K. K.; Wong, V.
- Meteorology and Atmospheric Physics, Vol. 75, Issue 3-4
A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows
journal, January 2014
- Yang, Chao; Cai, Xiao-Chuan
- SIAM Journal on Scientific Computing, Vol. 36, Issue 5
Works referencing / citing this record:
Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration
journal, May 2018
- Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.
- Journal of Scientific Computing, Vol. 77, Issue 2
Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration
preprint, January 2017
- Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.
- arXiv