I. Verification

5. Details of the benchmark numerical solution

The numerical values of the coefficients of polynomials describing profiles of the two velocity components and temperature for the selected benchmark solution (FRE6). The coefficients were obtained by nonlinear least-squares (NNLS) Marquardt-Levenberg algorithm. The order of polynomials was selected so that the remaining fit error (standard deviation relative to the maximum value) remained below 1%. 

 

X = 0.5

 

U

W

Temperature

a0

0.653255375988277

-0.0182133390825522

0.375731268271168

a1

-236.702203764653

-0.534506952806084

0.0646566206852292

a2

1443.71621734046

-4649.62374660758

-3.44261930694882

a3

-13999.9971459506

9166.34090898581

    80.5716617494023

a4

-48978.2873061909

184756.318840003

   -849.389178138508

A5

769502.177696391

-2267214.57474188

5426.31856180659

a6

-2826411.42861687

13921830.6389979

-20619.6870300723

a7

5049355.25968998

-50905496.7836152

47584.9389176856

a8

-4889309.49455426

117326421.048108

-66982.5680747791

a9

2473294.32955038

-175454949.94745

54146.8042661755

a10

-514661.642022168

170542299.447756

-18312.94874948

a11

 

-104264882.357183

-5638.00828334596

a12

 

36505160.4951902

6840.33395345218

a13

 

-5592440.58260601

-1672.49783568399



 

Y = 0.5

 

U

W

Temperature

a0

-0.971923736403444

1.00212115245059

0.999467521831559

a1

435.542611756185

12877.9988611009

-6.23069515529224

a2

-35897.4472988611

-259340.543848846

-18.9999577130502

a3

1124550.4608794

2053796.14649148

433.527770212382

a4

-19836290.5781327

-5602841.78532119

7318.66314332766

a5

217415780.824244

-30304885.3151783

-180265.707163689

a6

-1573770830.54861

358963997.276281

1714792.57838228

a7

7864305725.45593

-1697089432.98434

-9862261.15685317

a8

-27964717917.5742

4892293454.42925

38472869.7475459

a9

72090244360.2021

-9357882052.45715

-106665059.51901

a10

-135881981012.186

12081139841.5678

214297962.730994

a11

187042192305.203

-10321221406.5473

-313025047.586471

a12

-185722571203.416

5462280648.88341

328987879.084903

a13

129406337902.134

-1489621427.86707

 -242193161.156869

a14

-59987319824.8771

62096039.6233113

118435075.266555

a15

16604163672.9515

43140732.9300454

-34530031.2923873

a16

-2075551754.938

0.321619021644532

4539519.05438302




 

X = 0.9

 

U

W

Temperature

a0

1.37834316239398

     1.11560341761746

0.308900034946171

a1

869.803859921856

-682.103162659822

-0.574121199057708

a2

74379.0946531731

64546.3444091368

74.382226060503

a3

-3924258.51426546

-2657731.00888943

-3161.22612928187

a4

89435741.7003693

60098287.7693382

74817.9579968359

a5

-1217186200.6406

-822661490.080435

-1125745.01070913

a6

10971526417.6405

7425487150.03986

11435967.2156945

a7

-69219909243.1401

-46729243229.224

      -81662746.1201518

a8

316473663407.374

212583413470.936

421890116.068198

a9

-1072529330832.37

-715751344227.008

         1608940868.43137

a10

2732146343933.84

1809508968294.41

4588612041.2787

a11

-5267137304120.64

-3459353036180.82

-9850623665.12099

a12

7684697385210.4

5001906037363.17

15919604870.6355

a13

-8422179003474.85

-5429815720822.07

         -19229337194.963

a14

6816871501820.86

4350956298121.35

17073562106.7329

a15

-3949555692631.44

-2494534120078.54

-10804649895.8457

a16

1548473261831.82

967384927672.173

4608652340.13695

a17

-367847357872.57

-227214939183.605

-1186818611.97188

a18

39966515019.2774

24398428716.3919

139329555.368117




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