MUSCL scheme: Difference between revisions

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en>Dthomsen8
m clean up, typo(s) fixed: lmiter → limiter, , → , using AWB
en>Hanyu Ye
The full name of MUSCL has been corrected according to van Leer's original paper.
 
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In [[continuum mechanics]], a '''hydrostatic stress''' is an [[isotropic]] [[Stress (mechanics)|stress]] that is given by the weight of water above a certain point. It is often used interchangeably with "[[pressure]]" and is also known as confining stress, particularly in the field geomechanics. Its magnitude <math>\sigma_h</math> can be given by:
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:<math>\sigma_h = \displaystyle\sum_{i=1}^n \rho_i g h_i</math>
 
where <math>i</math> is an index denoting each distinct layer of material above the point of interest, <math>\rho_i</math> is the [[density]] of each layer, <math>g</math> is the [[gravitational acceleration]] (assumed constant here; this can be substituted with any [[acceleration]] that is important in defining [[weight]]), and <math>h_i</math> is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
 
:<math>\sigma_{h,sand} = \rho_w g h_w = 1000 \,\text{kg/m}^3 \cdot 9.8 \,\text{m/s}^2 \cdot 10 \,\text{m} = 9.8 \cdot {10^4} {kg/ms^2} = 9.8 \cdot 10^4 {N/m^2} </math>
 
where the index <math>w</math> indicates "water".
 
Because the hydrostatic stress is isotropic, it acts equally in all directions. In [[tensor]] form, the hydrostatic stress is equal to
 
:<math>\sigma_h \cdot I_3 =
\left[ \begin{array}{ccc}
\sigma_h & 0 & 0 \\
0 & \sigma_h & 0 \\
0 & 0 & \sigma_h \end{array} \right]
</math>
 
where <math>I_3</math> is the 3-by-3 [[identity matrix]].
 
[[Category:Continuum mechanics]]
[[Category:Orientation]]

Latest revision as of 10:44, 20 April 2014

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