[Getdp] Electrokinetic - GetDP vs. Analytical Solution

mail at jchn.de mail at jchn.de
Tue Jul 31 16:26:35 CEST 2012


Hello Everyone,



since a couple of days, I am comparing the solution of GetDP with the analytical
solution of a simple earthing arrangement.

There are two hemispheres, both have their origin in point (1)={0,0,0,lc1}, the
earth electrode (inner hemisphere) has a radius of r0 = 1 m, the reference
ground (outer hemisphere) has a radius of r1 = 200 m.

Between these hemispheres a current of -10 kA flows, the potential of the inner
hemisphere is set to 0 V (yes, really). The soil resistivity is set to rho = 30
Ohm*m.



The voltage at the outer hemisphere can be calculated as follows: U = I * rho /
2 / Pi * ( 1/r0 – 1/r1 ) = 47508 V



With the attached files, I get a result from GetDP of U = 44666 V



Is it possible that there’s something wrong with the meshing? I think the
deviation is too big to explain it with the different "solving procedure"...



Greetings,



Jochen





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Include "num.geo";

lc1=0.05;
lc2=5;

Point(1) = {0, 0, 0, lc1};
Point(2) = {0, -1, 0, lc1};
Point(3) = {1, 0, 0, lc1};
Point(4) = {-1, 0, 0, lc1};
Point(5) = {0, 0, 1, lc1};
Point(6) = {0, 0, -1, lc1};
Point(7) = {0, -200, 0, lc2};
Point(8) = {200, 0, 0, lc2};
Point(9) = {-200, 0, 0, lc2};
Point(10) = {0, 0, 200, lc2};
Point(11) = {0, 0, -200, lc2};
Circle(1) = {4, 1, 5};
Circle(2) = {5, 1, 3};
Circle(3) = {3, 1, 6};
Circle(4) = {6, 1, 4};
Circle(5) = {4, 1, 2};
Circle(6) = {6, 1, 2};
Circle(7) = {3, 1, 2};
Circle(8) = {5, 1, 2};
Circle(9) = {9, 1, 10};
Circle(10) = {10, 1, 8};
Circle(11) = {8, 1, 11};
Circle(12) = {11, 1, 9};
Circle(13) = {8, 1, 7};
Circle(14) = {9, 1, 7};
Circle(15) = {10, 1, 7};
Circle(16) = {11, 1, 7};
Line Loop(19) = {6, -7, 3};
Ruled Surface(20) = {19};
Line Loop(21) = {7, 2, -8};
Ruled Surface(22) = {21};
Line Loop(23) = {8, 1, -5};
Ruled Surface(24) = {23};
Line Loop(25) = {5, -6, 4};
Ruled Surface(26) = {25};
Line Loop(29) = {16, -13, 11};
Ruled Surface(30) = {29};
Line Loop(31) = {13, -15, 10};
Ruled Surface(32) = {31};
Line Loop(33) = {15, -14, 9};
Ruled Surface(34) = {33};
Line Loop(35) = {14, -16, 12};
Ruled Surface(36) = {35};
Line(39) = {11, 6};
Line(40) = {4, 9};
Line(41) = {10, 5};
Line(42) = {3, 8};
Line Loop(43) = {11, 39, -3, 42};
Ruled Surface(44) = {43};
Line Loop(45) = {42, -10, 41, 2};
Ruled Surface(46) = {45};
Line Loop(47) = {41, -1, 40, 9};
Ruled Surface(48) = {47};
Line Loop(49) = {40, -12, 39, 4};
Ruled Surface(50) = {49};
Surface Loop(51) = {46, 44, 30, 36, 34, 32, 48, 24, 22, 20, 26, 50};
Volume(52) = {51};
Physical Surface (Reference_Ground) = {30,32,34,36};
Physical Surface (Earth_Electrode) = {20,22,24,26};
Physical Volume (Soil) = {52};
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Include "num.geo";

// Group Data
// ===========
// 
Group{
Soil 				= #Soil;
Earth_Electrode 	= #Earth_Electrode;
Reference_Ground	= #Reference_Ground;

Int_Vol		= Region[{Soil}];
Elem_all	= Region[{Soil, Earth_Electrode, Reference_Ground}];
}

// Function
// ============
// 
Function{

rho[Soil]				= 30; //Ohm-Meters

Reference_Potential =	   0; //Volts
Earthing_Current = 	  -10000; //Ampere

}

// Constraint
// ==========
// 
Constraint{
	{Name Ref_Grnd; Type Assign;
	Case{
        {Region Earth_Electrode; Value Reference_Potential; }
		}
	}
}

// Jacobian
// =========
// 
Jacobian {
  { Name JVol ;
    Case {
      { Region All ; Jacobian Vol ; }
    }
  }
  { Name JSur ;
    Case {
      { Region All ; Jacobian Sur ; }
    }
  }
  { Name JLin ;
    Case {
      { Region All ; Jacobian Lin ; }
    }
  }
}

Include "Integration_Lib.pro"; // Same as in the Reference Manual

// FunctionSpace
// ==============
// 
FunctionSpace {
  { Name Funspc_Name ; Type Form0 ;
    BasisFunction {
      { Name sn ; NameOfCoef vn ; Function BF_Node ;
        Support Elem_all ; Entity NodesOf[ All, Not Reference_Ground ] ;} 
	  { Name sf; NameOfCoef vf; Function BF_GroupOfNodes;
        Support Elem_all ; Entity GroupsOfNodesOf[Reference_Ground]; }
	}
	GlobalQuantity {
           { Name GlobalCurrent; Type AliasOf; NameOfCoef vf; }
    }
    Constraint {
      { NameOfCoef vn ; EntityType NodesOf ;
        NameOfConstraint Ref_Grnd ;}
    }
  }
}

// Formulation
// ============
// 
Formulation{
  { Name Electrokinetics; Type FemEquation;
    Quantity{
      { Name v; Type Local; NameOfSpace Funspc_Name;}
	  { Name V; Type Global; NameOfSpace Funspc_Name [GlobalCurrent]; }
    }
    Equation {
      Galerkin { [ 1/rho[]*Dof{Grad v} , {Grad v} ]; In Int_Vol ;
                  Jacobian JVol ; Integration GradGrad ; }
	  GlobalTerm { [ -Earthing_Current, {V} ]; In Reference_Ground ; }
     }

  }
}

// Resolution
// ===========
//
Resolution{
  {Name EleKin_v;
    System{
      {Name Syst; NameOfFormulation Electrokinetics;}
    }
    Operation{
      Generate[Syst]; Solve[Syst]; SaveSolution[Syst];
    }
  }
}

// Post Processing
// ================
//
PostProcessing{
  {Name EleKin_v; NameOfFormulation Electrokinetics; NameOfSystem Syst;
    Quantity{
      {Name v; Value {Local{[{v}];In Elem_all;Jacobian JVol;}}}
    }
  }
}

// Post Operation
// ===============
// 
PostOperation{
  {Name Map_v; NameOfPostProcessing EleKin_v;
    Operation{
      Print[v, OnElementsOf Elem_all, File "Potential.pos"];
      Print [ v, OnLine { {0,0,0} {200,0,0} } {2000}, Format Table, File "Potential_rad.txt" ];
    }
  }
}
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Earth_Electrode		=	1001	;
Reference_Ground	=	1002	;
Soil				=	1003	;
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1951 0.4996975003033584 -0.7411190290107134 -0.4483804110672012
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1959 0.555566627534515 -0.397517927322033 -0.730291188381402
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1961 0.8098585858504958 -0.257431895426482 -0.5271222724770451
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1963 0.6652261929558102 -0.5352544213124384 -0.5205543359448714
1964 0.8380905482546859 -0.2669679409711103 -0.4757439977759106
1965 0.08601725977196234 -0.9247960338896974 -0.3706120973783885
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1968 0.6308375569925826 -0.3675982052236529 -0.6833121806348687
1969 0.4836456895577356 -0.3949257714348368 -0.7811020944977818
1970 0.104152581894977 -0.3855838997283066 -0.9167754883039364
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1977 0.5253695048667298 -0.6705174496278595 -0.5238255750730751
1978 0.3473079175672442 -0.7931482853691414 -0.5002929220077926
1979 0.3703950014270426 -0.0781456431619756 -0.925581331581759
1980 0.08870168307099924 -0.5308741616607519 -0.8427957260815732
1981 0.5750741482547133 -0.1500247967853348 -0.8042277565208968
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1984 0.8818616282452176 -0.4596306118876545 -0.1051654374995607
1985 0.550381050811533 -0.03730764770941197 -0.834079635484516
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1988 0.2589520624455379 -0.1539610561253169 -0.9535406769257299
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1990 0.2846390974145734 -0.4190197730878482 -0.862208219622398
1991 0.620066563980796 -0.5162965610895801 -0.5907244004103125
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1994 0.5602347029461132 -0.4865041752293727 -0.67041089273614
1995 0.6745452933475378 -0.4389419196069475 -0.5935643507105631
1996 0.6669062904833586 -0.5687568989622306 -0.4814058470735407
1997 0.8838020287796835 -0.1055495328998639 -0.4557995941524478
1998 0.9337765946944144 -0.3207521020391428 -0.1586800562086314
1999 0.03398323580223777 -0.670083405033973 -0.7415074982645057
2000 0.7817821884633859 -0.4692212161270871 -0.4106678221356239
2001 0.8345783564940325 -0.4236977178091619 -0.3520784156903513
2002 0.04022127354535189 -0.9315909680507218 -0.3612762342041186
2003 0.8636669736829127 -0.08550591834794606 -0.4967575832303656
2004 0.2227425911008451 -0.1173883647675496 -0.9677839169602286
2005 0.9686742265106826 -0.1473111753992591 -0.1999241368530065
2006 0.5619521136076959 -0.5904428946626709 -0.5792987227279286
2007 0.06898931415486048 -0.8931162165250997 -0.444504103819451
2008 0.9293350903079638 -0.1304972393436472 -0.3454081070935881
2009 0.291776899577296 -0.2503756624613118 -0.9231350218251498
2010 0.3401281659194066 -0.5334626481513459 -0.7744226454434644
2011 0.6689676516774901 -0.3484705479464111 -0.6565444068934196
2012 0.9446091268815431 -0.1317929428341074 -0.3005731485532508
2013 0.5150550600895831 -0.1568192931169649 -0.8426897379121283
2014 0.3787361828957541 -0.2796507959593281 -0.8822439209679305
2015 0.6912144637213572 -0.04585158886945032 -0.7211935918604266
2016 0.2635730068141213 -0.2094646245062346 -0.9416229824932192
2017 0.5290300151307738 -0.4761394071947196 -0.7024375474068809
2018 0.9536762400141418 -0.2875226887303721 -0.08850046721767531
2019 0.5207037539811256 -0.405486119647112 -0.7512979484621873
2020 0.3031857170954568 -0.7714907284932316 -0.5593571996482178
2021 0.9727421032484095 -0.04091004942619513 -0.2282524226022741
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