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# Class Note for BSysE 595 at WSU 08

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Washington State University taught by a professor in Fall. Since its upload, it has received 30 views.

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Date Created: 02/06/15
Numerical Solutions and MODFLOW Development of FiniteDifference Equation for Laplace Equation The Laplace equation for 261 homogeneous isotropic porous medium is 62h 62h 6x2 6y2 0 1 Consider the first term in 1 that is defined as Q limhxAx9 hx9y 6x Ax v0 Ax As it is impossible to take the limit on a digital computer we have to approximate the limit by assigning to Ax a small value e g designing a nodal network with a mesh spacing Ax For any y value yo expand hxy0 in a Taylor s expansion about point x0y0 as 8h hx9yo hx09y0 x x0 Eocosyo x xo2 62h 2 6x2 x0y0 2 Let x x0 Ax forward difference and drop all the terms of order greater than unity we have ah hx0 9yo hx0 y0 xoy0 Ax ax 3 Q What do the dropped terms represent Similarly a backward difference approximation forx x0 Ax is ah hx0ay0 hxo Axay0 axxoy0 Ax 4 2 To obtain the approximation for write a 6x2 forwarddifference equation in terms of x ah ah x Ax x 82 1106 2 axo yo axoy0 6x2 myo Ax 5 Then substitute the backwarddifference expression of Eq 4 into Eq 5 to obtain 62h hx Myhxy 2x0 y0 0 0 2 0 0 8x Ax hx09yo hx0 Axayo sz hx0 Ax9y02hxosy0hx0 Ax9y0 A362 6 2 Similarly the difference expression for M is By2 82h 2x0 y0 6y h xo yo Ay 2h xo y0 h xoayo Ay Ayz 7 For a square grid Ax Ay adding 6 and 7 yields 1 quot3905 Axsy hx Axsy M2 0 0 0 0 hx09yo Ay hx09yo Ay 4h xoayon 0 8 Let x0y0 be the nodal point i j Eq 8 becomes 1 hm Zmi j hi Lj hij1 hiJl 2 MODFLOW A finitedifference computer model Simulate 3d transientstate ow Use blockcentered nodes Dimensions of each cell can be varied de facto standard code for aquifer simulation Robust wellcrafted product Excellent manual documentation Adequate technical support by the USGS Modular structure allowing addition of new modules

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