Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning

Ghosh, Debojyoti; Constantinescu, Emil M.

doi:10.1137/15M1044369

Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning

Journal Article · Thu Jun 23 00:00:00 EDT 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/15M1044369· OSTI ID:1362122

Ghosh, Debojyoti ^[1]; Constantinescu, Emil M. ^[1]

Argonne National Lab. (ANL), Lemont, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1362122

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 38; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

References (49)

Euler solutions using flux-based wave decomposition Ahmad, Nash'at; Lindeman, John International Journal for Numerical Methods in Fluids, Vol. 54, Issue 1 https://doi.org/10.1002/fld.1392	journal	January 2007
Weighted Essentially Non-oscillatory Schemes Liu, Xu-Dong; Osher, Stanley; Chan, Tony Journal of Computational Physics, Vol. 115, Issue 1 https://doi.org/10.1006/jcph.1994.1187	journal	November 1994
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows Bonaventura, Luca Journal of Computational Physics, Vol. 158, Issue 2 https://doi.org/10.1006/jcph.1999.6414	journal	March 2000
Multirate linear multistep methods Gear, C. W.; Wells, D. R. BIT, Vol. 24, Issue 4 https://doi.org/10.1007/BF01934907	journal	December 1984
A nonhydrostatic model based on a new approach Janjic, Z. I. Meteorology and Atmospheric Physics, Vol. 82, Issue 1-4 https://doi.org/10.1007/s00703-001-0587-6	journal	January 2003
An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models Gassmann, A. Meteorology and Atmospheric Physics, Vol. 88, Issue 1-2 https://doi.org/10.1007/s00703-003-0053-8	journal	May 2004
The Advanced Regional Prediction System (ARPS) - A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification Xue, M.; Droegemeier, K. K.; Wong, V. Meteorology and Atmospheric Physics, Vol. 75, Issue 3-4 https://doi.org/10.1007/s007030070003	journal	December 2000
Multirate infinitesimal step methods for atmospheric flow simulation Wensch, Jörg; Knoth, Oswald; Galant, Alexander BIT Numerical Mathematics, Vol. 49, Issue 2 https://doi.org/10.1007/s10543-009-0222-3	journal	April 2009
Multirate Timestepping Methods for Hyperbolic Conservation Laws Constantinescu, Emil M.; Sandu, Adrian Journal of Scientific Computing, Vol. 33, Issue 3 https://doi.org/10.1007/s10915-007-9151-y	journal	September 2007
Multirate Explicit Adams Methods for Time Integration of Conservation Laws Sandu, Adrian; Constantinescu, Emil M. Journal of Scientific Computing, Vol. 38, Issue 2 https://doi.org/10.1007/s10915-008-9235-3	journal	August 2008
Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows Ghosh, Debojyoti; Baeder, James D. Journal of Scientific Computing, Vol. 61, Issue 1 https://doi.org/10.1007/s10915-014-9818-0	journal	January 2014
Approximate Riemann solvers, parameter vectors, and difference schemes Roe, P. L. Journal of Computational Physics, Vol. 43, Issue 2 https://doi.org/10.1016/0021-9991(81)90128-5	journal	October 1981
Compact finite difference schemes with spectral-like resolution Lele, Sanjiva K. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90324-R	journal	November 1992
The calculation of the interaction of non-stationary shock waves and obstacles Rusanov, V. V. USSR Computational Mathematics and Mathematical Physics, Vol. 1, Issue 2 https://doi.org/10.1016/0041-5553(62)90062-9	journal	January 1962
Additive Runge–Kutta schemes for convection–diffusion–reaction equations Kennedy, Christopher A.; Carpenter, Mark H. Applied Numerical Mathematics, Vol. 44, Issue 1-2 https://doi.org/10.1016/S0168-9274(02)00138-1	journal	January 2003
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations Ascher, Uri M.; Ruuth, Steven J.; Spiteri, Raymond J. Applied Numerical Mathematics, Vol. 25, Issue 2-3 https://doi.org/10.1016/S0168-9274(97)00056-1	journal	November 1997
A semi-implicit time-splitting scheme for a regional nonhydrostatic atmospheric model Bourchtein, Andrei; Bourchtein, Ludmila Computer Physics Communications, Vol. 183, Issue 3 https://doi.org/10.1016/j.cpc.2011.12.001	journal	March 2012
Well balanced finite volume methods for nearly hydrostatic flows Botta, N.; Klein, R.; Langenberg, S. Journal of Computational Physics, Vol. 196, Issue 2 https://doi.org/10.1016/j.jcp.2003.11.008	journal	May 2004
An anelastic allspeed projection method for gravitationally stratified flows Gatti-Bono, Caroline; Colella, Phillip Journal of Computational Physics, Vol. 216, Issue 2 https://doi.org/10.1016/j.jcp.2005.12.017	journal	August 2006
A time-split nonhydrostatic atmospheric model for weather research and forecasting applications Skamarock, William C.; Klemp, Joseph B. Journal of Computational Physics, Vol. 227, Issue 7 https://doi.org/10.1016/j.jcp.2007.01.037	journal	March 2008
A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases Giraldo, F. X.; Restelli, M. Journal of Computational Physics, Vol. 227, Issue 8 https://doi.org/10.1016/j.jcp.2007.12.009	journal	April 2008
Partially implicit peer methods for the compressible Euler equations Jebens, Stefan; Knoth, Oswald; Weiner, Rüdiger Journal of Computational Physics, Vol. 230, Issue 12 https://doi.org/10.1016/j.jcp.2011.03.015	journal	June 2011
A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics Smolarkiewicz, Piotr K.; Kühnlein, Christian; Wedi, Nils P. Journal of Computational Physics, Vol. 263 https://doi.org/10.1016/j.jcp.2014.01.031	journal	April 2014
Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X. Journal of Computational Physics, Vol. 301 https://doi.org/10.1016/j.jcp.2015.07.034	journal	November 2015
Operator-Based Preconditioning of Stiff Hyperbolic Systems Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S. SIAM Journal on Scientific Computing, Vol. 32, Issue 1 https://doi.org/10.1137/080713331	journal	January 2010
Extrapolated Implicit-Explicit Time Stepping Constantinescu, Emil M.; Sandu, Adrian SIAM Journal on Scientific Computing, Vol. 31, Issue 6 https://doi.org/10.1137/080732833	journal	January 2010
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling Giraldo, F. X.; Restelli, M.; Läuter, M. SIAM Journal on Scientific Computing, Vol. 32, Issue 6 https://doi.org/10.1137/090775889	journal	January 2010
Compact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws Ghosh, Debojyoti; Baeder, James D. SIAM Journal on Scientific Computing, Vol. 34, Issue 3 https://doi.org/10.1137/110857659	journal	January 2012
Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA) Giraldo, F. X.; Kelly, J. F.; Constantinescu, E. M. SIAM Journal on Scientific Computing, Vol. 35, Issue 5 https://doi.org/10.1137/120876034	journal	January 2013
A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows Yang, Chao; Cai, Xiao-Chuan SIAM Journal on Scientific Computing, Vol. 36, Issue 5 https://doi.org/10.1137/130919167	journal	January 2014
Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed SIAM Journal on Scientific Computing, Vol. 37, Issue 3 https://doi.org/10.1137/140989261	journal	January 2015
The Simulation of Three-Dimensional Convective Storm Dynamics Klemp, Joseph B.; Wilhelmson, Robert B. Journal of the Atmospheric Sciences, Vol. 35, Issue 6 https://doi.org/10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;2	journal	June 1978
A Non-Archimedean Approach to the Equations of Convection Dynamics Das, Phanindramohan Journal of the Atmospheric Sciences, Vol. 36, Issue 11 https://doi.org/10.1175/1520-0469(1979)036<2183:ANAATT>2.0.CO;2	journal	November 1979
A Semi-Implicit Scheme for grid Point Atmospheric Models of the Primitive Equations Kwizak, Michael; Robert, AndrÉ J. Monthly Weather Review, Vol. 99, Issue 1 https://doi.org/10.1175/1520-0493(1971)099<0032:ASSFGP>2.3.CO;2	journal	January 1971
Efficiency and Accuracy of the Klemp-Wilhelmson Time-Splitting Technique Skamarock, William C.; Klemp, Joseph B. Monthly Weather Review, Vol. 122, Issue 11 https://doi.org/10.1175/1520-0493(1994)122<2623:EAAOTK>2.0.CO;2	journal	November 1994
The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) Hodur, Richard M. Monthly Weather Review, Vol. 125, Issue 7 https://doi.org/10.1175/1520-0493(1997)125<1414:TNRLSC>2.0.CO;2	journal	July 1997
Conservative Scheme for the Compressible Nonhydrostatic Models with the Horizontally Explicit and Vertically Implicit Time Integration Scheme Satoh, Masaki Monthly Weather Review, Vol. 130, Issue 5 https://doi.org/10.1175/1520-0493(2002)130<1227:CSFTCN>2.0.CO;2	journal	May 2002
Time-Splitting Methods for Elastic Models Using Forward Time Schemes Wicker, Louis J.; Skamarock, William C. Monthly Weather Review, Vol. 130, Issue 8 https://doi.org/10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2	journal	August 2002
Explicit Two-Step Peer Methods for the Compressible Euler Equations Jebens, Stefan; Knoth, Oswald; Weiner, Rüdiger Monthly Weather Review, Vol. 137, Issue 7 https://doi.org/10.1175/2008MWR2671.1	journal	July 2009
A Two-Step Adams–Bashforth–Moulton Split-Explicit Integrator for Compressible Atmospheric Models Wicker, Louis J. Monthly Weather Review, Vol. 137, Issue 10 https://doi.org/10.1175/2009MWR2838.1	journal	October 2009
Operator-Split Runge–Kutta–Rosenbrock Methods for Nonhydrostatic Atmospheric Models Ullrich, Paul; Jablonowski, Christiane Monthly Weather Review, Vol. 140, Issue 4 https://doi.org/10.1175/MWR-D-10-05073.1	journal	April 2012
Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems Durran, Dale R.; Blossey, Peter N. Monthly Weather Review, Vol. 140, Issue 4 https://doi.org/10.1175/MWR-D-11-00088.1	journal	April 2012
A Blended Soundproof-to-Compressible Numerical Model for Small- to Mesoscale Atmospheric Dynamics Benacchio, Tommaso; O’Neill, Warren P.; Klein, Rupert Monthly Weather Review, Vol. 142, Issue 12 https://doi.org/10.1175/MWR-D-13-00384.1	journal	December 2014
Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves Weller, Hilary; Shahrokhi, Ava Monthly Weather Review, Vol. 142, Issue 12 https://doi.org/10.1175/MWR-D-14-00054.1	journal	December 2014
An Implicitly Balanced Hurricane Model with Physics-Based Preconditioning Reisner, J. M.; Mousseau, A.; Wyszogrodzki, A. A. Monthly Weather Review, Vol. 133, Issue 4 https://doi.org/10.1175/MWR2901.1	journal	April 2005
Application of Compact-Reconstruction Weighted Essentially Nonoscillatory Schemes to Compressible Aerodynamic Flows Ghosh, Debojyoti; Medida, Shivaji; Baeder, James D. AIAA Journal, Vol. 52, Issue 9 https://doi.org/10.2514/1.J052654	journal	September 2014
Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows Ghosh, Debojyoti; Constantinescu, Emil M. AIAA Journal, Vol. 54, Issue 4 https://doi.org/10.2514/1.J054580	journal	April 2016

Cited By (2)

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R. Journal of Scientific Computing, Vol. 77, Issue 2 https://doi.org/10.1007/s10915-018-0726-6	journal	May 2018
Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R. arXiv https://doi.org/10.48550/arxiv.1707.08247	preprint	January 2017

Similar Records

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

Journal Article · Fri May 11 20:00:00 EDT 2018 · Journal of Scientific Computing · OSTI ID:1458696

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Journal Article · Thu Nov 30 23:00:00 EST 2023 · Monthly Weather Review · OSTI ID:2580154

Semi-implicit magnetohydrodynamic calculations

Journal Article · Mon Jun 01 00:00:00 EDT 1987 · J. Comput. Phys.; (United States) · OSTI ID:6604224

Related Subjects

54 ENVIRONMENTAL SCIENCES
97 MATHEMATICS AND COMPUTING
Euler equations
atmospheric flows
characteristic-based splitting
compressible
implicit-explicit time integration
nonhydrostatic

Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning

Citation Formats

References (49)

Cited By (2)

Similar Records

Related Subjects