chapter_benchmarks.tex

\chapter{Geodynamical/geophysical benchmarks \label{sec:geobench}}

\begin{flushright} {\tiny {\color{gray} \tt chapter\_benchmarks.tex}} \end{flushright}

%=======================================
\section{Benchmarks organised by topics}

Some published numerical experiments have over time become benchmarks for the entire
community. I present in what follows a short list of `famousx' benchmarks' in the 
computational geodynamics community.

%-----------------------------------
\subsection{Subduction}

\begin{itemize}
\item subduction problems: \textcite{spka06} (2006), \textcite{scbe08} (2008), 
                           \textcite{vack08} (2008), \textcite{cehg14} (2014),
                           \textcite{gltf18} (2018), \textcite{ozrs08} (2008),
                           \textcite{siwi20} (2020).

\item Benchmark of 3D numerical models of subduction against a laboratory experiment: 
      Meriaux \etal (2018)  \cite{memm18}

\end{itemize}

%-----------------------------------
\subsection{Stokes sphere \& sinkers}

\begin{itemize}
\item the Stokes sphere: Gale manual \cite{galemanual}, 
      \aspect{} manual \cite{aspectmanual}, 
      in visco-plastic fluid: \textcite{limd02} (2002), 
      \textcite{demj04} (2004). 
      Finite deformation in and around a fluid sphere \cite{sccm88,crud88}.

\item the sinking block (sinker) 
      \textcite{thie11} (2011),
      \textcite{cehg14} (2014),
      \textcite{gery10} (2010),
      \textcite{geyu03} (2003),
      \textcite{mamo08} (2008),
      \textcite{mishin11} (2011),
      \textcite{fumt11} (2011),
      \textcite{maie12} (2012),
      \textcite{sctc20} (2020),
      \textcite{mivg22} (2022). 
      (see Section~\ref{sec:sinker})

\item multiple sinkers \cite{mabl14,mabl15,clhe21,rusg17}

\item Sinking cylinder (2D Stokes sphere): 
      appendix A of \cite{boht08a}, \cite{wali04}.
      Wall correction factor for sinking cylinders in fluids \cite{rist97}.

\item hot blob problem \cite{bugs09,fumt11} (see Section~\ref{sec:hotblob})

\item Semi-analytical solution for viscous Stokes flow in two eccentrically
nested spheres \cite{toma07}

\item Two circular cylinders in viscous fluid: \textcite{waki75a,waki75b} (1975).

\end{itemize}


%-----------------------------------
\subsection{(Visco-)Elastic deformation}

\begin{itemize}

\item bending of elastic plate/beam \cite{cehg14,boht08a,vosc15,elga10,demh19,modm02,litu02}

\item flexure of finite length elastic plate \cite{chtl13}

\item stress build-up in Maxwell visco-elastic material 
      \cite{geyu07,chtl13,elga10,demh19}
\item single layer visco-elastic folding \cite{scps01,vosc15}
\item viscous(-elastic) flow around a cylinder in a channel (see Section~\ref{sec:flowcyl})
\item Semi-infinite elastic half plane with a circular hole \cite{verr98}
\item Uniform strip load on elastic material (see Section~\ref{sec:elaststripload})
\item Jull and McKenzie (1996) \cite{jumc96} parabolic load on viscoelastic half-space (and melt fractions) 
\item Stress distribution in elastic sphere under equal and 
      opposite loads \cite{stro52}
\item Love's problem: Becker \& Bevis (2004) \cite{bebe04}
\item Infinite plate with a circular hole \cite{yiha10,rama16}
\item Square plate with a crack subjected to a horizontal tensile 
      traction \cite{litu02}
\item Hollow sphere under internal pressure, see Section~\ref{ss:hollowsphereintpress}
\end{itemize}

%-----------------------------------
\subsection{Convection}

\begin{itemize}
\item 2D Rayleigh-Benard convection (see Section~\ref{ss:blbc89}).

\item 2D Rayleigh-Benard convection, lateral heating, 30+ codes: 
      \textcite{dejo83} (1983).

\item 2D Rayleigh-Benard convection with nonlinear rheology:  
      \textcite{tosn15} (2015), \aspect{} manual \cite{aspectmanual}, 
      \textcite{trbs21} (2021), \stone~28, \textcite{dakg22} (2022),
      \textcite{siwi20} (2020), \textcite{casd20} (2020).

\item 3D convection at infinite Prandtl number with modest viscosity variation:
      \textcite{bucc94} (1994),
      \textcite{trha98} (1998),
      \textcite{kaks05} (2005),
      \textcite{onmm06} (2006),
      \textcite{krhb12} (2012), 
      \textcite{trbs21} (2021),
      \textcite{dakg22} (2022).
      This benchmark is carried out in Stone~\ref{f20}.

      \begin{center}
      \includegraphics[height=4cm]{images/busse93/kaks05}
      \includegraphics[height=4cm]{images/busse93/krhb12}\\
      {\captionfont Left: Taken from Kameyama \etal (2005).
      a) Isothermal surfaces obtained for the benchmark calculations 
      of stationary convections in Busse \etal. (1993). (a) Case 1a is for
      constant viscosity, while (b) Case 2 is for modestly temperature-dependent 
      viscosity whose viscosity contrast is 20. The calculations
      were carried out with (a) 64x32x64 and (b) 64x64x64 mesh divisions.
      Right: Taken from Kronbichler \etal (2012).}
      \end{center}

\item Numerical simulations of three-dimensional thermal convection 
      in a fluid with strongly
      temperature-dependent viscosity: Ogawa \etal \cite{ogsz91,kaks05} 

\item Convection in 2D-box \cite{galb19} (see Section~\ref{sec:citb})

\item Onset of convection \cite{aspectmanual}

\item mantle convection in 3D spherical shell:
      \textcite{rasz96} (1996),
      \textcite{iwas96} (1996),
      \textcite{zhzm00} (2000),
      \textcite{yoka04} (2004),
      \textcite{sthh06} (2006),
      \textcite{chcc07} (2007),
      \textcite{zhmt08} (2008),
      \textcite{hust08b} (2008),
      \textcite{kaks08} (2008),
      \textcite{wrfy10} (2010),
      \textcite{dadb13} (2013),
      \textcite{hutm13} (2013),
      \textcite{busa13} (2013),
      \textcite{arfw14} (2014),
      \textcite{liki19} (2019),
      \textcite{trbs21} (2021),
      \textcite{eulg23} (2023),
      \textcite{ildk24} (ildk24).

\item Mantle convection with reversing mobile plates \cite{kogk05} (2005).

\item A comparison of mantle convection models featuring plates \cite{stlh14} (2014).

\end{itemize}

%-----------------------------------
\subsection{Free surface \& interfaces}

\begin{itemize}

\item Free surface evolution: Crameri \etal (2012) \cite{crsg12}, 
      \aspect{} manual \cite{aspectmanual}, \textcite{sctc20} (2020).

\item relaxation of sinusoidal interface \cite{crsg12,robh17}

\end{itemize}


%-----------------------------------
\subsection{Rayleigh-Taylor}

\begin{itemize}
\item 2D Rayleigh-Taylor convection/instability:\\ 
      \textcite{pros81} (1981),
      \textcite{trab90} (1990),
      \textcite{wesc92} (1992),
      \textcite{popo92} (1992),
      \textcite{ogaw93} (1993),
      \textcite{como97} (1997),
      \textcite{vaks97} (1997),
      \textcite{devv00a} (2000),
      \textcite{soga01} (2001),
      \textcite{bast02} (2002),
      \textcite{taki03} (2003),
      \textcite{bomh06} (2006),
      \textcite{dadh07} (2007),
      \textcite{basd08} (2008),
      \textcite{deka08} (2008),
      \textcite{qurj09} (2009),
      \textcite{saev10} (2010),
      \textcite{sunh10} (2010),
      \textcite{lezh11} (2011),
      \textcite{thie11} (2011),
      \textcite{mishin11} (2011), 
      \textcite{lomw12} (2012), 
      \textcite{maie12} (2012),
      \textcite{fusc13} (2013), 
      \textcite{vyrc13} (2013), 
      \textcite{chtl13} (2013),
      \textcite{ropu19} (2019),
      \textcite{robe19} (2019), 
      \textcite{demh19} (2019),
      \textcite{logb20} (2020),
      \textcite{sctc20} (2020),
      \textcite{mivg22} (2022),
      \textcite{buoa24} (2024),
      \aspect manual \cite{aspectmanual}.

\item 3D Rayleigh-Taylor instability:
      \textcite{fukk08} (2008),
      \textcite{vosc15} (2015).

\item Polydiapirism \cite{wesc92,aspectmanual}

\end{itemize}

%-----------------------------------
\subsection{Couette \& Poiseuille flow}

\begin{itemize}
\item Couette flow with temperature dependent viscosity \cite{elga10,demh19}
\item Couette flow with shear heating \cite{elga10}
\item Couette flow of a power-law fluid, Section 2.4 of  \textcite{saramito}
\item Poiseuille flow: \cite{fojg94,fuku11,tagm09} (see Section~\ref{ss:poiseuille})
\item Poiseuille-Couette flow: \textcite{fusc13} (2013)
\item Poiseuille flow of a power-law fluid, Section 2.3 of  \textcite{saramito}
\item Channel flow: \textcite{manc08} (2008)
\item channel flow (nonlinear): \cite{geyu03,maie12,frbt19,gery10,elga10}
\item Squeezing flow between moving parallel plates: \textcite{gugu77} (1977)
\item Flow of a Power Law Fluid Through a Tube - page 87 of \textcite{macosko}
\end{itemize}



%-----------------------------------
\subsection{Thermal problems}

\begin{itemize}
\item thermal diffusion of half-cooling space (see Section~\ref{sec:hcsp}) 
\item thermal diffusion of Gaussian distribution (see compgeo notes, elefant manual)
\item Heat flow around a cylinder (see Section~\ref{sec:hfcyl})
\end{itemize}

%-----------------------------------
\subsection{Lid driven cavity problems}

\begin{itemize}
\item Lid driven cavity 
      \textcite{kawa61} (1961),
      \textcite{chor67} (1967),
      \textcite{shry78} (1978),
      \textcite{foth79} (1979),
      \textcite{ghgs82} (1982),
      \textcite{kost84} (1984),
      \textcite{bope98} (1998),
      \textcite{xika01} (2001),
      \textcite{brsa06} (2006),
      \textcite{ertu09} (2009),
      \textcite{tesk12} (2012).

\item Lid driven cavity with analytical solution (see Section~\ref{sec:ldc_anal})

\item Lid driven cavity with nonlinear rheology \cite{been80,svna18}
\end{itemize}

%-----------------------------------
\subsection{Visco-plastic problems}

\begin{itemize}

\item the 'plastic brick' (See section~\ref{ss:plasticbrick}): \\
      \textcite{lemm08} (2008), 
      \textcite{qurj09} (2009), 
      \textcite{kaus10} (2010), 
      \textcite{mishin11} (2011), 
      \textcite{muso11} (2011), 
      \textcite{maie12} (2012), 
      \textcite{spmw16} (2016), 
      \textcite{kapb16} (2016), 
      \textcite{gltf18} (2018), 
      \textcite{frbt19} (2019),
      \textcite{mivg22} (2022).

\item indentor, punch problem (see Section~\ref{sec:punch}):\\
      \textcite{vidm82} (1982),
      \textcite{vidm84} (1984),
      \textcite{vimd86} (1986),
      \textcite{gepd98} (1998),
      \textcite{hukm03} (2003), 
      \textcite{fojd04} (2004), 
      \textcite{thfb08} (2008),
      \textcite{gerb12} (2012), 
      \textcite{gltf18} (2018).

\item numerical sandbox \cite{bube06,bube06,maie12,busa16,gltf18}

\item fractal networks of shear bands: \textcite{pohe94} (1994)

\end{itemize}


%-----------------------------------
\subsection{Miscellaneous}

\begin{itemize}

\item 2D Rayleigh-Benard laminar plumes, comparison of laboratory 
      and numerical modeling : 
      \textcite{vavl09} (2009
)
\item 2D Cartesian flow with extremely temperature-dependent viscosity:
      \textcite{moso95} (1995), \textcite{trbs21} (2021).

\item Thin layer entrainment (see Section~\ref{sec:tlentr})

\item 1D compression \cite{modm02}

\item 2D compressible Stokes flow problem 
      \cite{itki94,tagu07,lezh08,kilv10,lizh13,lee_13}

\item Wannier flow \cite{wann50,yemu99,cehg14}

\item plastic oedometer test  \cite{chtl13}

\item Three-dimensional folding of an embedded viscous layer in 
      pure shear \cite{flet91}

\item dam-break problem 
      \cite{moeb99,bacp07,liir07,lemx08,homa09,anco09,grdn97,hini81,basd08}

\item Slope stability for elasto-plastic materials \cite{rama16}

\item Time-dependent flow in an annulus \cite{galb19} (see Section \ref{sec:tdba})

\item Slab detachment benchmark (see Section~\ref{sec:slabdetach}) 

\item 3D Hollow sphere Stokes flow benchmark:\\
      Thieulot (2017) \cite{thie17},
      Horbach \etal (2020) \cite{homb20},
      Kramer \etal \cite{krdw21}

\item Axisymmetric hollow sphere compressible Stokes flow benchmark:\\
      Machetel \& yuen (1989) \cite{mayu89}

\item Annulus benchmark \cite{aspectmanual}, \cite{ples11}

\item Viscosity grooves benchmark \cite{aspectmanual}

\item Latent heat benchmark \cite{aspectmanual}

\item Layered flow with viscosity contrast \cite{aspectmanual} 
      (see Section \ref{sec:layfl}) 

\item Brittle thrust wedges benchmark \cite{busa16,aspectmanual}

\item Laplace equation on a semi infinite plate (see Section~\ref{sec:lapplate})

\item 2D Stokes flow over cavity: Popov \& Makeev (2014) \cite{poma14}.

\item Analytical solution for solitary porosity waves: \textcite{copo15} (2015)

\item Analytical solution for solitary wave of magma: Dannberg \& Heister (2016) \cite{dahe16} and refs therein

\item Stokes flow caused by the motion of a rigid sphere close 
      to a viscous interface: \textcite{dagr98} (1998)

\item Deformation caused by a closed vertical volcanic pipe \cite{boda99}

\item Linear Stability Analysis for Thermal Convections in 
      Spherical Shells \textcite{yuwa19} (2019)

\item Viscous half-space loading \cite{hask35}

\item Nakiboglu and Lambeck (1982) has cylindrical load on variety of rheologies \cite{nala82}

\item generalized half-plane and half-space Cerruti \cite{nowi92,zhga15}

\item Analytical Solutions of Displacements Produced by spherically-shaped Internal Overpressure \cite{gech12}

\item Sagging viscous bridge \cite{stokes98}

\item Deformation around a terminating fault in a viscous medium \cite{baho96}

\end{itemize}





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