skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1];  [1]
  1. 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. https://doi.org/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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

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
  • DOI: 10.1002/fld.1392

Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
journal, November 1997


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
  • DOI: 10.1175/MWR-D-13-00384.1

Well balanced finite volume methods for nearly hydrostatic flows
journal, May 2004


A semi-implicit time-splitting scheme for a regional nonhydrostatic atmospheric model
journal, March 2012


Multirate Timestepping Methods for Hyperbolic Conservation Laws
journal, September 2007


Extrapolated Implicit-Explicit Time Stepping
journal, January 2010

  • Constantinescu, Emil M.; Sandu, Adrian
  • SIAM Journal on Scientific Computing, Vol. 31, Issue 6
  • DOI: 10.1137/080732833

A Non-Archimedean Approach to the Equations of Convection Dynamics
journal, November 1979


Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems
journal, April 2012


An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models
journal, May 2004


An anelastic allspeed projection method for gravitationally stratified flows
journal, August 2006


Multirate linear multistep methods
journal, December 1984


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
  • DOI: 10.1137/110857659

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows
journal, January 2014


Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows
journal, April 2016

  • Ghosh, Debojyoti; Constantinescu, Emil M.
  • AIAA Journal, Vol. 54, Issue 4
  • DOI: 10.2514/1.J054580

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
  • DOI: 10.1137/140989261

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
  • DOI: 10.2514/1.J052654

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
  • DOI: 10.1137/120876034

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
  • DOI: 10.1137/090775889

A nonhydrostatic model based on a new approach
journal, January 2003


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
  • DOI: 10.1175/2008MWR2671.1

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
  • DOI: 10.1016/j.jcp.2011.03.015

Efficient Implementation of Weighted ENO Schemes
journal, June 1996

  • Jiang, Guang-Shan; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 126, Issue 1
  • DOI: 10.1006/jcph.1996.0130

Additive Runge–Kutta schemes for convection–diffusion–reaction equations
journal, January 2003


The Simulation of Three-Dimensional Convective Storm Dynamics
journal, June 1978


A Semi-Implicit Scheme for grid Point Atmospheric Models of the Primitive Equations
journal, January 1971


Compact finite difference schemes with spectral-like resolution
journal, November 1992


Weighted Essentially Non-oscillatory Schemes
journal, November 1994

  • Liu, Xu-Dong; Osher, Stanley; Chan, Tony
  • Journal of Computational Physics, Vol. 115, Issue 1
  • DOI: 10.1006/jcph.1994.1187

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
  • DOI: 10.1016/j.jcp.2015.07.034

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
  • DOI: 10.1175/MWR2901.1

Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981


The calculation of the interaction of non-stationary shock waves and obstacles
journal, January 1962


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
  • DOI: 10.1137/0907058

Efficiency and Accuracy of the Klemp-Wilhelmson Time-Splitting Technique
journal, November 1994


A time-split nonhydrostatic atmospheric model for weather research and forecasting applications
journal, March 2008


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
  • DOI: 10.1016/j.jcp.2014.01.031

Operator-Split Runge–Kutta–Rosenbrock Methods for Nonhydrostatic Atmospheric Models
journal, April 2012


Multirate infinitesimal step methods for atmospheric flow simulation
journal, April 2009


A Two-Step Adams–Bashforth–Moulton Split-Explicit Integrator for Compressible Atmospheric Models
journal, October 2009


Time-Splitting Methods for Elastic Models Using Forward Time Schemes
journal, August 2002


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
  • DOI: 10.1007/s007030070003

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
  • DOI: 10.1137/130919167

    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
    • DOI: 10.1007/s10915-018-0726-6