Semi-implicit predictor-corrector methods for atmospheric models

Slides:

Advertisements

Similar presentations

Finite Difference Discretization of Hyperbolic Equations: Linear Problems Lectures 8, 9 and 10.

Advertisements

ECMWF Governing Equations 3 Slide 1 Numerical methods IV (time stepping) by Nils Wedi (room 007; ext. 2657) In part based on previous material by Mariano.

The equations of motion and their numerical solutions I by Nils Wedi (2006) contributions by Mike Cullen and Piotr Smolarkiewicz.

PARMA UNIVERSITY SIMULATIONS OF THE ISOLATED BUILDING TEST CASE F. AURELI, A. MARANZONI & P. MIGNOSA DICATeA, Parma University Parco Area delle Scienze.

A High-Order Finite-Volume Scheme for the Dynamical Core of Weather and Climate Models Christiane Jablonowski and Paul A. Ullrich, University of Michigan,

Reduction of Temporal Discretization Error in an Atmospheric General Circulation Model (AGCM) Daisuke Hotta Advisor: Prof. Eugenia Kalnay.

(c) MSc Module MTMW14 : Numerical modelling of atmospheres and oceans Staggered schemes 3.1 Staggered time schemes.

WWOSC 2014 Montreal, Canada Running operational Canadian NWP models on next-generation supercomputers Michel Desgagné, Abdessamad Qaddouri, Janusz.

Krakow - September, 15th 2008COSMO WG 2 - Runge Kutta1 Further Developments of the Runge-Kutta Time Integration Scheme Investigation of Convergence (task.

Jan Verwer Convergence and Component Splitting for the Crank-Nicolson Leap-Frog Scheme Hairer-60 Conference, Geneva, June 2009 TexPoint fonts used in EMF.

A Semi-Lagrangian Laplace Transform Filtering Integration Scheme Colm Clancy and Peter Lynch Meteorology & Climate Centre School of Mathematical Sciences.

Network and Grid Computing –Modeling, Algorithms, and Software Mo Mu Joint work with Xiao Hong Zhu, Falcon Siu.

Finite Difference Methods to Solve the Wave Equation To develop the governing equation, Sum the Forces The Wave Equation Equations of Motion.

Ordinary Differential Equations (ODEs)

Solution of the Implicit Formulation of High Order Diffusion for the Canadian Atmospheric GEM Model “High Performance Computing and Simulation Symposium.

© Arturo S. Leon, BSU, Spring 2010

Towards Developing a “Predictive” Hurricane Model or the “Fine-Tuning” of Model Parameters via a Recursive Least Squares Procedure Goal: Minimize numerical.

A Look at High-Order Finite- Volume Schemes for Simulating Atmospheric Flows Paul Ullrich University of Michigan.

Most physically significant large-scale atmospheric circulations have time scales on the order of Rossby waves but much larger than the time scales.

C M C C Centro Euro-Mediterraneo per i Cambiamenti Climatici COSMO General Meeting - September 8th, 2009 COSMO WG 2 - CDC 1 An implicit solver based on.

Comparison of convective boundary layer velocity spectra calculated from large eddy simulation and WRF model data Jeremy A. Gibbs and Evgeni Fedorovich.

A cell-integrated semi-Lagrangian dynamical scheme based on a step-function representation Eigil Kaas, Bennert Machenhauer and Peter Hjort Lauritzen Danish.

IMEX Methods for Advection-Diffusion-Reaction Equations Eindhoven 2008 Speaker : Volha Shchetnikava Adviser: dr.ir.J.H.M. ten Thije Boonkkamp.

Efficient Integration of Large Stiff Systems of ODEs Using Exponential Integrators M. Tokman, M. Tokman, University of California, Merced 2 hrs 1.5 hrs.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. ~ Ordinary Differential Equations ~ Stiffness and Multistep.

3.3.3: Semi-Lagrangian schemes AOSC614 class Hong Li.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 261 Stiffness.

The equations of motion and their numerical solutions II by Nils Wedi (2006) contributions by Mike Cullen and Piotr Smolarkiewicz.

Numerical simulations of inertia-gravity waves and hydrostatic mountain waves using EULAG model Bogdan Rosa, Marcin Kurowski, Zbigniew Piotrowski and Michał.

WORKSHOP ON LONG-WAVE RUNUP MODELS Khairil Irfan Sitanggang and Patrick Lynett Dept of Civil & Ocean Engineering, Texas A&M University.

Two Dimensional simulation of a Dam Break wave propagation for the isolated building test case University of Pavia Gabriella Petaccia Impact Workshop...

Numerical Analysis – Differential Equation

International Workshop on Long-Wave Runup Models 2-Dimensional Model with Boundary-Fitting Cell System Benchmark #2:Tsunami Runup onto a Complex 3Dimensional.

AMS 691 Special Topics in Applied Mathematics Lecture 8

Discretization for PDEs Chunfang Chen,Danny Thorne Adam Zornes, Deng Li CS 521 Feb., 9,2006.

On the mechanism of eastward-propagation of super cloud clusters (SCCs) over the equator – Impact of precipitation activities on climate of East Asia –

Instability in Leapfrog and Forward-Backward Schemes by Wen-Yih Sun Department of Earth and Atmospheric Sciences Purdue University West Lafayette, IN.

Standardized Test Set for Nonhydrostatic Dynamical Cores of NWP Models

Modeling orographic flows on unstructured meshes Piotr Smolarkiewicz, National Center for Atmospheric Research*, USA; Joanna Szmelter, Loughborough University,

Numerics of Parametrization ECMWF training course May 2006 by Nils Wedi  ECMWF.

Global variable-resolution semi-Lagrangian model SL-AV: current status and further developments Mikhail Tolstykh Institute of Numerical Mathematics, Russian.

Performance of a Semi-Implicit, Semi-Lagrangian Dynamical Core for High Resolution NWP over Complex Terrain L.Bonaventura D.Cesari.

1 On forward in time differencing: an unstructured mesh framework Joanna Szmelter Piotr Smolarkiewicz Loughborough University NCAR UK Colorado USA.

Priority project CDC Task 1.4: Choice of the anelastic equation system and Milestone 3.2: Suitability of fundamental approximations PP CDC-Meeting, ,

Solving Ordinary Differential Equations

Loughborough University, UK

The semi-Lagrangian semi-implicit technique in the ECMWF model

A Proposed Test Suite for Atmospheric Model Dynamical Cores

Reporter: Prudence Chien

Lecture 4: Numerical Stability

A Semi-Lagrangian Laplace Transform Filtering Integration Scheme

Loughborough University, UK

Conservative Dynamical Core (CDC)

NUMERICAL INVESTIGATIONS OF FINITE DIFFERENCE SCHEMES

Perturbation equations for all-scale atmospheric dynamics

Adaptive Grids in Climate Modeling: Dynamical Core Tests

Finite Volume Method for Unsteady Flows

AIAA OBSERVATIONS ON CFD SIMULATION UNCERTAINITIES

AIAA OBSERVATIONS ON CFD SIMULATION UNCERTAINTIES

Objective Numerical methods Finite volume.

Bogdan Rosa1, Marcin Kurowski1, Damian Wójcik1,

Investigators Tony Johnson, T. V. Hromadka II and Steve Horton

High Accuracy Schemes for Inviscid Traffic Models

Need for Numerical Developments within COSMO J

Comparison of CFEM and DG methods

MATH 175: NUMERICAL ANALYSIS II

Conservative Dynamical Core (CDC)

6th Lecture : Numerical Methods

Presentation transcript:

Semi-implicit predictor-corrector methods for atmospheric models Colm Clancy Janusz A. Pudykiewicz Atmospheric Numerical Weather Prediction Research, Environment Canada PDEs on the Sphere, 26th of September 2012

Motivation Development of a finite-volume atmospheric model on an icosahedral grid (Pudykiewicz 2006, 2011) Investigation of stable time integration schemes, beyond the traditional semi-implicit leapfrog Some recent work: Williams (2011), Durran & Blossey (2012), Kar (2012)

General ODE system

General ODE system ‘Traditional’ semi-implicit, (SILF):

Semi-implicit predictor-corrector approach Predictor stage, for : Corrector stage, for :

Implicit linear terms: Trapezoidal AM2*

Explicit nonlinear terms:

Many possible combinations… Examples:

Linear stability analysis

Reference semi-implicit

Shallow water tests Shallow water model of Pudykiewicz (2011) Iterative GCR(4) solver for Helmholtz equations (Smolarkiewicz and Margolin, 2000) No explicit diffusion Filter of Williams (2011) for the semi-implicit leapfrog Spatial resolution: grid 6 (40,962 nodes, ~112km). Reference: grid 7 (163,842 nodes, ~56km) with RK4 at 90s time-step

Sample results: Flow over isolated mountain

Williamson et al. (1992) – Mountain case

Williamson et al. (1992) – Mountain case

Williamson et al. (1992) – Mountain case

Sample results: Rossby-Haurwitz wave

Williamson et al. (1992) – RH wave case

Williamson et al. (1992) – RH wave case

Williamson et al. (1992) – RH wave case

Efficiency Predictor-corrector schemes: two elliptic solver calls per time-step Consider total number of iterations per step

Efficiency

Conclusions and further work Semi-implicit predictor-corrector schemes offer an accurate alternative to the traditional leapfrog: Stable No time filter necessary Efficiency not affected Future tests with a three-dimensional baroclinic model Comparison with other time integration methods

References Clancy & Pudykiewicz (2012); to appear in J. Comp. Phys. Durran & Blossey (2012); Mon. Weather. Rev. 140, 1307-1325 Kar (2012); Mon. Weather. Rev. 134, 2916-2926 Pudykiewicz (2006); J. Comp. Phys. 213, 358-390 Pudykiewicz (2011); J. Comp. Phys. 230, 1956-1991 Smolarkiewicz & Margolin (2000). Proc. ECWMF Workshop, 5-7 June 2000, 137-159 Williams (2011); Mon. Weather. Rev. 139, 1996-2007 Williamson et al. (1992); J. Comp. Phys. 102, 211-224

Many possible combinations…