Differential Quadrature Solution for One-Dimensional Aquifer Flow

Abstract

Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage, were examined. The results of DQM solution were then compared with the results obtained from analytical solution, the Explicit Finite Differences Method and Implicit Finite Differences Method. Based on the comparison results, it was concluded that the DQM provides similar results but with relatively faster calculation speed, less nodes and memory usage.

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

“… n j i w , weighting coefficients, () [34]; Chen and Yongxi [35]) are used as the test functions to determine the weighting coefficients:…”

“…Further developments achieved by Shu et al [7] based on Polynomial-based differential quadrature, (PDQ) (Shu and Richards [8]; Shu et al [9] ), Fourier expansion-based differential quadrature (FDQ) ( Shu and Xue [10]; Shu and Chew [11]) and RBF-DQ based on Radial Basis Function, (Shu et al [12], [13]). Now DQM has been applied successfully in many fields such as fluid dynamics (Shu et al [14], [15]; Tsai et al [16]), solid mechanics (Wang et al [17]), chemical engineering (Civan,[18]; Li and Mulay [19]), vibration and buckling (Mahmoud et al [20]; Danesh et al [21]), Geotechnics (Chen et al [22]), mass transfer (Char et al [23]). In groundwater fields, Kaya and Arisoy [24] used DQM to solve three one-dimensional aquifer flow equation problems including a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage.…”

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

“…Differential quadrature method has also been used in different fields of fluid mechanics . In hydraulic and free surface water flow fields, the work completed by Kaya et al to solve a flood propagation problem in open channel, Kaya and Arisoy to solve the Saint‐Venant equations for linear long wave propagation in open channels, Hashemi et al to modeling long waves in shallow water and tidal and surge using incremental DQM, and Hashemi et al to solve the Saint‐Venant equations for numerical simulation of unsteady open channel flow can be pointed out.…”

“…They concluded that DQM has the ability to simulate water surface profile and results are very close to the real water surface profile. Kaya and Arisoy used DQM to solve three one‐dimensional aquifer flow equation problems including a confined aquifer flow with time‐dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage.…”

توسعه ی روش دیفرانسیل کوادراچر در شبیه‌سازی جریان تک فاز در محیط متخلخل مخازن هیدروکربنی

“…; u=}QH p=Ut pL QO DQ VwQ OQ@Q=m |xv}tR QO VmyR p=v=m wO u}@ ? ; K]U p}iwQB |x@U=Lt CyH 2009 p=U QO |WywSB PDQ VwQ R= xO=iDU= =@ '2011 p=U QO u}= Q@ xwqa [16] "OQm xQ=W= |v}tRQ} R =@ xDU@ u=wN@; u=}QH pt=W |Oa@l} u=wN@; u=}QH |xrUt`wv 3 pL x@ xDN=OQB uoty=v |xDU@ w R=@ |=yu=wN@; R= CWv w u=tR x@ xDU@=w |RQt \}=QW |=yVwQ w |r}rLD pL R= pY=L G}=Dv =@ PDQ VwQ G}=Dv xm CU= xOW xOt; CUOx@ |@ wN j@=]D w xOW xU}=kt 7 FDM OwOLt p[=iD K} QY |vt[ [17] "CU= DQ VwQ R= xO=iDU= =@ TmwDU=Q} w=v CqO=at pL w |UQQ@ QO u}vJty DQ VwQ uOw@QFwt p=L u}a QO w |oO=U Qov=}@ xOt; CUOx@ G}=Dv '2013 |DQ=QL p}rLD w |UQQ@ QO R}v '2016 p=U QO [18] [7] "OyO|t QO [8] [20] [22] 'uJ |xOWx= Q= OwOLt p[=iD =@ swO |xrUt =Pr 'Ow@ Q}PBsm = QD |D@=F MQv =@ swO |xrUt QO uRNt nvU xmv}= x@ '…”