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revision 1.24 by mlosch, Tue Sep 15 13:31:19 2015 UTC revision 1.25 by mlosch, Tue Mar 29 14:50:54 2016 UTC
# Line 602  the damping time scale $T$ accordingly, Line 602  the damping time scale $T$ accordingly,
602  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly  $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly
603  \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.  \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
604    
605  \paragraph{More stable variant of Elastic-Viscous-Plastic Dynamics:  EVP*\label{sec:pkg:seaice:EVPstar}}~\\  \paragraph{More stable variants of Elastic-Viscous-Plastic Dynamics:
606      EVP* , mEVP, and aEVP \label{sec:pkg:seaice:EVPstar}}~\\
607  %  %
608  The genuine EVP schemes appears to give noisy solutions \citep{hun01,  The genuine EVP schemes appears to give noisy solutions \citep{hun01,
609    lemieux12, bouillon13}. This has lead to a modified EVP or EVP*    lemieux12, bouillon13}. This has lead to a modified EVP or EVP*
610  \citep{lemieux12, bouillon13, kimmritz15}; here, refer to these  \citep{lemieux12, bouillon13, kimmritz15}; here, we refer to these
611  variants by EVP*. The main idea is to modify the ``natural''  variants by modified EVP (mEVP) and adaptive EVP (aEVP)
612    \citep{kimmritz16}. The main idea is to modify the ``natural''
613  time-discretization of the momentum equations:  time-discretization of the momentum equations:
614  \begin{equation}  \begin{equation}
615    \label{eq:evpstar}    \label{eq:evpstar}
# Line 642  replace the time stepping parameters \co Line 644  replace the time stepping parameters \co
644  speed of convergence and the stability. Usually, it makes sense to use  speed of convergence and the stability. Usually, it makes sense to use
645  $\alpha = \beta$, and \code{SEAICEnEVPstarSteps} $\gg  $\alpha = \beta$, and \code{SEAICEnEVPstarSteps} $\gg
646  (\alpha,\,\beta)$ \citep{kimmritz15}. Currently, there is no  (\alpha,\,\beta)$ \citep{kimmritz15}. Currently, there is no
647  termination criterion and the number of EVP* iterations is fixed to  termination criterion and the number of mEVP iterations is fixed to
648  \code{SEAICEnEVPstarSteps}.  \code{SEAICEnEVPstarSteps}.
649    
650  In order to use EVP* in the MITgcm, set \code{SEAICEuseEVPstar =  In order to use mEVP in the MITgcm, set \code{SEAICEuseEVPstar =
651    .TRUE.,} in \code{data.seaice}. If \code{SEAICEuseEVPrev =.TRUE.,}    .TRUE.,} in \code{data.seaice}. If \code{SEAICEuseEVPrev =.TRUE.,}
652  the actual form of equations (\ref{eq:evpstarsigma}) and  the actual form of equations (\ref{eq:evpstarsigma}) and
653  (\ref{eq:evpstarmom}) is used with fewer implicit terms and the factor  (\ref{eq:evpstarmom}) is used with fewer implicit terms and the factor
# Line 653  of $e^{2}$ dropped in the stress equatio Line 655  of $e^{2}$ dropped in the stress equatio
655  and (\ref{eq:evpstresstensor12}). Although this modifies the original  and (\ref{eq:evpstresstensor12}). Although this modifies the original
656  EVP-equations, it turns out to improve convergence \citep{bouillon13}.  EVP-equations, it turns out to improve convergence \citep{bouillon13}.
657    
658  Note, that for historical reasons, \code{SEAICE\_deltaTevp} needs to  Another variant is the aEVP scheme \citep{kimmritz16}, where the value
659  be set to some (any!) value in order to use also EVP*; this behavoir  of $\alpha$ is set dynamically based on the stability criterion
660  many change in the future. Also note, that  \begin{equation}
661  probably because of the C-grid staggering of velocities and stresses,    \label{eq:aevpalpha}
662  EVP* does not converge as successfully as in \citet{kimmritz15}.    \alpha = \beta = \max\left( \tilde{c}\pi\sqrt{c \frac{\zeta}{A_{c}}
663        \frac{\Delta{t}}{\max(m,10^{-4}\text{\,kg})}},\alpha_{\min} \right)
664    \end{equation}
665    with the grid cell area $A_c$ and the ice and snow mass $m$.  This
666    choice sacrifices speed of convergence for stability with the result
667    that aEVP converges quickly to VP where $\alpha$ can be small and more
668    slowly in areas where the equations are stiff. In practice, aEVP leads
669    to an overall better convergence than mEVP \citep{kimmritz16}.
670    %
671    To use aEVP in the MITgcm set \code{SEAICEaEVPcoeff} $= \tilde{c}$;
672    this also sets the default values of \code{SEAICEaEVPcStar} ($c=4$)
673    and \code{SEAICEaEVPalphaMin} ($\alpha_{\min}=5$). Good convergence
674    has been obtained with setting these values \citep{kimmritz16}:
675    \code{SEAICEaEVPcoeff = 0.5, SEAICEnEVPstarSteps = 500,
676      SEAICEuseEVPstar = .TRUE., SEAICEuseEVPrev = .TRUE.}
677    
678    Note, that probably because of the C-grid staggering of velocities and
679    stresses, mEVP may not converge as successfully as in
680    \citet{kimmritz15}, and that convergence at very high resolution
681    (order 5\,km) has not been studied yet.
682    
683  \paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\  \paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\
684  %  %
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