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RebelYoung

沉了么。。？有大佬试试我的算例了么？

RebelYoung

250m/s的cube，60步出现negative initial temperature。

# Field minima and maxima
# Time        	field         	min           	location(min) 	max           	location(max) 
3.57143e-05   	T             	1.454278e+02	(1.646393e-02 1.393888e-19 -1.709886e-18)	3.108947e+02	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.57143e-05   	e             	1.043157e+05	(1.646393e-02 1.393888e-19 -1.709886e-18)	2.230054e+05	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.64286e-05   	T             	1.335562e+02	(5.517241e-03 1.105814e-02 1.105814e-02)	3.098790e+02	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.64286e-05   	e             	9.580017e+04	(5.517241e-03 1.105814e-02 1.105814e-02)	2.222768e+05	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.71429e-05   	T             	2.917792e+01	(6.206897e-03 1.105814e-02 1.105814e-02)	3.078215e+02	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.71429e-05   	e             	2.092939e+04	(6.206897e-03 1.105814e-02 1.105814e-02)	2.208010e+05	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.58333e-05   	T             	1.400088e+02	(5.517241e-03 1.105814e-02 1.179091e-02)	3.108729e+02	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.58333e-05   	e             	1.004286e+05	(5.517241e-03 1.105814e-02 1.179091e-02)	2.229898e+05	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.65278e-05   	T             	6.218740e+01	(5.517241e-03 1.105814e-02 1.105814e-02)	3.097428e+02	(-1.646393e-02 1.393888e-19 -1.725321e-18)
3.65278e-05   	e             	4.460715e+04	(5.517241e-03 1.105814e-02 1.105814e-02)	2.221792e+05	(-1.646393e-02 1.393888e-19 -1.725321e-18)

最后几步的温度最值，最后两步$T_{min}$下降一个量级。

RebelYoung

@东岳我是用pointwise画了导出的，这个球比较难画，
我的另一个简单算例cube (提取码: ywvc)是有附面层的全结构网格，上传的设置是初始条件是类似rhoS的0012算例的freestream type。
来流速度30m/s，就是上面贴图的龟派气功的结果，在几百步后也会发散，出现负温度。

RebelYoung

@东岳重新试了一下250m/s，相当于0.83Ma，算了20步就出现负初始温度的问题

RebelYoung

https://www.cfd-china.com/topic/1737/可压缩求解器为什么密度残差一直为0-迭代步也一直是0

这里面回答了rho，rhoE，rhoU残差为0的原因。

RebelYoung

@东岳那么高速导致雷诺数量级太大，层流模型还能算么？

RebelYoung

@东岳我其他的边界条件pT都是一样的，控制雷诺数，计算了不同的速度。因为是层流，所以上传的是最小速度1m/s的。

RebelYoung

@东岳是的哇

RebelYoung

尝试画粗网格计算正方体外流，结果确实可以计算，deltat=10^-7算到0.05s，未出现以上问题。
对应精细网格，计算到300个时间步，又出现了温度陡增的发散问题。

细网格内能残差

粗网格内能残差

两个算例的迭代中能量残差都是initial residual< final residual，不过粗网格没有发散。
在这些rhoC算例中计算发现，温度压强都有“龟派气功”的特效。。。前缘驻点附近形成的高压会脱体。。。后缘驻点类似。。。

到最后消失了。。。

RebelYoung

算例文件在文中已经贴出

RebelYoung

计算目的：计算跨声速外流，先尝试简单模型计算，尝试使用rhoCentralFoam求解器。

算例外形	球
直径	0.002m。
边界条件	自由流
来流速度	1到250m/s均有计算
压强	6.0e4 Pa
温度	270K
流体类型	标准气体

网格为非结构，prism附面层。
条件根据rhoC的tutorials算例修改。

首先说一下在rhoC的tutorials算例发现的几个现象：

所有rhoC的tutorials算例均为laminar。
所有rhoC的tutorials算例计算中输出的：

diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoUx, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoUy, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoE, Initial residual = 0, Final residual = 0, No Iterations 0

残差始终为0。和我计算中一致，不知道这是什么问题。
3. 有些算例为了控制Mach数，速度温度都设置的很低，看似是低速但是马赫数很高。但是这些算例中的rho/rhoU/rhoE的残差也始终是0。

rcf_sphere算例(提取码: b7h6)出现的问题：Negative Initial Temperature

报错如下：

--> FOAM FATAL ERROR: 
Negative initial temperature T0: -10272.9

    From function Foam::scalar Foam::species::thermo<Thermo, Type>::T(Foam::scalar, Foam::scalar, Foam::scalar, Foam::scalar (Foam::species::thermo<Thermo, Type>::*)(Foam::scalar, Foam::scalar) const, Foam::scalar (Foam::species::thermo<Thermo, Type>::*)(Foam::scalar, Foam::scalar) const, Foam::scalar (Foam::species::thermo<Thermo, Type>::*)(Foam::scalar) const, bool) const [with Thermo = Foam::hConstThermo<Foam::perfectGas<Foam::specie> >; Type = Foam::sensibleInternalEnergy; Foam::scalar = double; Foam::species::thermo<Thermo, Type> = Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy>]
    in file /home/rebel/OpenFOAM/OpenFOAM-7/src/thermophysicalModels/specie/lnInclude/thermoI.H at line 56.

FOAM aborting

#0  Foam::error::printStack(Foam::Ostream&) at ??:?
#1  Foam::error::abort() at ??:?
#2  Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy>::T(double, double, double, double (Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy>::*)(double, double) const, double (Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy>::*)(double, double) const, double (Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy>::*)(double) const, bool) const at ??:?
#3  Foam::hePsiThermo<Foam::psiThermo, Foam::pureMixture<Foam::constTransport<Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy> > > >::calculate() at ??:?
#4  Foam::hePsiThermo<Foam::psiThermo, Foam::pureMixture<Foam::constTransport<Foam::species::thermo<Foam::hConstThermo<Foam::perfectGas<Foam::specie> >, Foam::sensibleInternalEnergy> > > >::correct() at ??:?
#5  ? in "/home/rebel/OpenFOAM/OpenFOAM-7/platforms/linux64GccDPInt32Opt/bin/rhoCentralFoam"
#6  __libc_start_main in "/lib/x86_64-linux-gnu/libc.so.6"
#7  ? in "/home/rebel/OpenFOAM/OpenFOAM-7/platforms/linux64GccDPInt32Opt/bin/rhoCentralFoam"

该错误往往发生在计算几十到一百个时间步后出现，根据残差可以发现和算例的区别是，每步的initial residuals都比final residuals大，而tutorials算例都是减小的，符合收敛的趋势。
但是，奇怪的是每一步的初始残差又总是只有10^-7^量级，也并不是很大。迭代后往往上升两个量级。。
其中内能e的上升比较明显，能从10^-9^上升到10^-5^。
所以光看残差趋势是预想不到某一步的直接发散。

之后增加minMax函数监视，发现在接近发散的几个时间步，最大内能和温度都会陡增。从约200K增加到2000多K。
但是由于时间步长太短，几十步发散的情况下，可视化后处理看不出什么道道。球表面像长痘痘一样出现一些高温点。这是说明附面层网格出毛病了？？
Alt
总的来说，应该就是能量方程发散，出现非物理的内能/温度。

另外，fvOptions限制器已经加了，不过没起作用。。。。

请问这个负初始温度到底是啥？以及解决办法。

谢谢谢！

还有两个小个问题是，
1.上面报错的一堆“#：：？？？” ，这堆报错信息到底能看出啥呀？这里面的问号是我电脑乱码了吗？
2.为什么同样laminar，同样的求解器，在不同算例里fvsolution中设置的量不同呢？
我是根据obliqueShock算例修改的，只是改了polyMesh和0文件下边界条件。可是运行报错e未定义，但是原算例本来就没有哇。

RebelYoung

最新看到的说法是，T估算值或者插值中出现了问题。比如方程解的是h，那么从h=cp(T)T中解出T的估算值，结果是负的。。
rhoC解的是e，那么e=CvT，cv基本不变，那应该是e出现负值导致T出现负值。。。

RebelYoung

@bestucan 可是上面minMax监视的全场温度，并没有出现负温度啊？初始值220K，最低也就210.。。

RebelYoung

以上基本描述的都是rhoCentralFoam问题，报错是Negative Initial Temperature，但是全场最小温度并没有负值。。
这个rcf_sphere_laminar是根据，$FOAM_TUTORIALS/compressible/rhoCentralFoam/obliqueShock改的。是层流计算，/0下设置了p，T，U三个量。
以下贴出rhoC 0下文件：
./0/p

FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [1 -1 -2 0 0 0 0];

internalField   uniform 100000;

boundaryField
{
    ball
    {
        type            zeroGradient;
    }

    inlet
    {
        type            zeroGradient;
    }

    outlet
    {
        type            fixedValue;
        value           uniform 100000;
    }

    far
    {
        type            zeroGradient;
    }
}

./0/T

FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      T;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 0 0 1 0 0 0];

internalField   uniform 270;

boundaryField
{
    ball
    {
        type            zeroGradient;
    }

    inlet
    {
        type            fixedValue;
        value           uniform 270;
    }

    outlet
    {
        type            zeroGradient;
    }

    far
    {
        type            fixedValue;
        value           uniform 270;
    }
}

./0/U
其中U从1到250，都算过。都出现能量方程发散或negative initial temperature问题。

FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (1 0 0);

boundaryField
{
    ball
    {
        type            noSlip;
    }

    inlet
    {
        type            fixedValue;
        value           uniform (1 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    
    far
    {
        type            fixedValue;
        value           uniform (1 0 0);
    }
}

checkMesh结果：

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create polyMesh for time = 0

Time = 0

Mesh stats
    points:           28680
    faces:            309924
    internal faces:   293684
    cells:            150902
    faces per cell:   4
    boundary patches: 4
    point zones:      0
    face zones:       0
    cell zones:       0

Overall number of cells of each type:
    hexahedra:     0
    prisms:        0
    wedges:        0
    pyramids:      0
    tet wedges:    0
    tetrahedra:    150902
    polyhedra:     0

Checking topology...
    Boundary definition OK.
    Cell to face addressing OK.
    Point usage OK.
    Upper triangular ordering OK.
    Face vertices OK.
    Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces...
    Patch               Faces    Points   Surface topology                  
    ball                9780     4892     ok (closed singly connected)      
    far                 4404     2278     ok (non-closed singly connected)  
    inlet               1028     553      ok (non-closed singly connected)  
    outlet              1028     553      ok (non-closed singly connected)  

Checking geometry...
    Overall domain bounding box (-0.1 -0.1 -0.1) (0.1 0.1 0.1)
    Mesh has 3 geometric (non-empty/wedge) directions (1 1 1)
    Mesh has 3 solution (non-empty) directions (1 1 1)
    Boundary openness (1.54762e-16 -1.49987e-17 -1.09064e-16) OK.
    Max cell openness = 3.03063e-16 OK.
    Max aspect ratio = 5.29154 OK.
    Minimum face area = 3.38388e-08. Maximum face area = 0.000137468.  Face area magnitudes OK.
    Min volume = 4.46514e-12. Max volume = 4.98913e-07.  Total volume = 0.00799582.  Cell volumes OK.
    Mesh non-orthogonality Max: 58.0988 average: 22.4508
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.67456 OK.
    Coupled point location match (average 0) OK.

Mesh OK.

End

@sibo

./constant/thermophysicalProperties: 此文件根据rhoS中计算翼型的文件修改，因为原算例是想控制mach数等原因，改的不符合物理性质，且mu=0。我将其改成了正常参数。

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "constant";
    object      thermophysicalProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

thermoType
{
    type            hePsiThermo;
    mixture         pureMixture;
    transport       const;
    thermo          hConst;
    equationOfState perfectGas;
    specie          specie;
    energy          sensibleInternalEnergy;
}

mixture
{
    // normalised gas
    specie
    {
        molWeight       28.9;
    }
    thermodynamics
    {
        Cp              1005;
        Hf              0;
    }
    transport
    {
        mu              1.8e-5;
        Pr              0.71;
    }
}

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "constant";
    object      turbulenceProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

simulationType  laminar;

RebelYoung

@sibo 上面传了个rcf_sphere_laminar 的压缩文件，里面有polyMesh 以外的文件。BCs 的话真的很简单，上面描述过了。

RebelYoung

@sibo log是rhoC 的，算例thermo 中mu 1.82E -5，肯定是viscous 哇。
一开始我算的超过0.3Ma ，很快发散。我怀疑是雷诺数太高的层流问题。。。就把速度改小了，雷诺数在10的3次方量级。

RebelYoung

log.zip
上传一个log文件。。。

RebelYoung

观察输出的迭代信息，发现，U rhoU rhoE三个值始终残差为0，我以为是不需要设置求解的，尝试在fvsolution中注销掉了，发现计算运行时会报错，说这几个量没有定义。。。定义了好像又不求解。。这是怎么回事呢？
而且我rcf迭代中，final残差总是比final残差大。。几个量级。。
并发现，上一步的final并不是下一步的initial残差。这是怎么回事呀？
初始残差一般都是10的-7量级，怎么迭代后越来越大，但是下一步的初始残差还是e-7。。。要被虐哭了，大佬帮帮我。

deltaT = 8.38392e-08
Mean and max Courant Numbers = 0.010868 0.525071
Time = 4.93006e-07

diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoUx, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoUy, Initial residual = 0, Final residual = 0, No Iterations 0
diagonal:  Solving for rhoUz, Initial residual = 0, Final residual = 0, No Iterations 0
smoothSolver:  Solving for Ux, Initial residual = 6.98094e-07, Final residual = 3.53286e-05, No Iterations 1000
smoothSolver:  Solving for Uy, Initial residual = 6.01407e-06, Final residual = 5.40888e-05, No Iterations 1000
smoothSolver:  Solving for Uz, Initial residual = 2.91948e-06, Final residual = 2.84312e-05, No Iterations 1000
diagonal:  Solving for rhoE, Initial residual = 0, Final residual = 0, No Iterations 0
smoothSolver:  Solving for e, Initial residual = 7.3214e-08, Final residual = 0.000463259, No Iterations 1000
ExecutionTime = 48.36 s  ClockTime = 54 s

RebelYoung

rcf_sphere_laminar.zip
@sibo 这里面差个polyMesh，那个文件有点大。

RebelYoung

残差监视，也没有过高量级的残差。。。

# Residuals   
# Time        	rho           	Ux            	Uy            	Uz            	rhoUx         	rhoUy         	rhoUz         	e             	rhoE          
1.2e-07       	0.000000e+00	9.999998e-01	9.999987e-01	9.999987e-01	0.000000e+00	0.000000e+00	0.000000e+00	7.969064e-06	0.000000e+00
2.20464e-07   	0.000000e+00	2.111891e-06	1.380125e-05	4.022545e-06	0.000000e+00	0.000000e+00	0.000000e+00	1.313458e-07	0.000000e+00
3.19452e-07   	0.000000e+00	1.264645e-06	1.060253e-05	3.560864e-06	0.000000e+00	0.000000e+00	0.000000e+00	1.072603e-07	0.000000e+00
4.09167e-07   	0.000000e+00	8.909982e-07	7.791157e-06	3.130739e-06	0.000000e+00	0.000000e+00	0.000000e+00	8.653875e-08	0.000000e+00
4.93006e-07   	0.000000e+00	6.980943e-07	6.014070e-06	2.919484e-06	0.000000e+00	0.000000e+00	0.000000e+00	7.321404e-08	0.000000e+00
5.72842e-07   	0.000000e+00	5.830812e-07	4.767039e-06	2.802532e-06	0.000000e+00	0.000000e+00	0.000000e+00	6.407240e-08	0.000000e+00
6.49727e-07   	0.000000e+00	5.076418e-07	3.877868e-06	2.757184e-06	0.000000e+00	0.000000e+00	0.000000e+00	5.741409e-08	0.000000e+00
7.24235e-07   	0.000000e+00	4.533701e-07	3.258493e-06	2.747260e-06	0.000000e+00	0.000000e+00	0.000000e+00	5.230926e-08	0.000000e+00
7.96689e-07   	0.000000e+00	4.120860e-07	2.797531e-06	2.719957e-06	0.000000e+00	0.000000e+00	0.000000e+00	4.823362e-08	0.000000e+00
8.6744e-07    	0.000000e+00	3.798487e-07	2.445596e-06	2.661090e-06	0.000000e+00	0.000000e+00	0.000000e+00	4.496448e-08	0.000000e+00
9.36681e-07   	0.000000e+00	3.528057e-07	2.173716e-06	2.574432e-06	0.000000e+00	0.000000e+00	0.000000e+00	4.225028e-08	0.000000e+00
1.00439e-06   	0.000000e+00	3.283802e-07	1.954853e-06	2.469235e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.986102e-08	0.000000e+00
1.07061e-06   	0.000000e+00	3.059676e-07	1.783138e-06	2.365464e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.775424e-08	0.000000e+00
1.13543e-06   	0.000000e+00	2.856882e-07	1.649840e-06	2.271488e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.591306e-08	0.000000e+00
1.19901e-06   	0.000000e+00	2.679408e-07	1.542351e-06	2.183317e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.432737e-08	0.000000e+00
1.26153e-06   	0.000000e+00	2.527546e-07	1.454461e-06	2.101230e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.297916e-08	0.000000e+00
1.32317e-06   	0.000000e+00	2.397965e-07	1.381828e-06	2.032610e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.182791e-08	0.000000e+00
1.38406e-06   	0.000000e+00	2.287559e-07	1.318413e-06	1.970739e-06	0.000000e+00	0.000000e+00	0.000000e+00	3.082433e-08	0.000000e+00
1.44424e-06   	0.000000e+00	2.191165e-07	1.260639e-06	1.915664e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.992920e-08	0.000000e+00
1.50377e-06   	0.000000e+00	2.106629e-07	1.207516e-06	1.863491e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.911098e-08	0.000000e+00
1.56264e-06   	0.000000e+00	2.031014e-07	1.158085e-06	1.805849e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.835210e-08	0.000000e+00
1.62088e-06   	0.000000e+00	1.962955e-07	1.112931e-06	1.741463e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.764534e-08	0.000000e+00
1.67851e-06   	0.000000e+00	1.900939e-07	1.072154e-06	1.669848e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.698383e-08	0.000000e+00
1.73554e-06   	0.000000e+00	1.844539e-07	1.034941e-06	1.592339e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.636862e-08	0.000000e+00
1.79202e-06   	0.000000e+00	1.793699e-07	1.000207e-06	1.511384e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.580314e-08	0.000000e+00
1.84798e-06   	0.000000e+00	1.747606e-07	9.661514e-07	1.428961e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.527796e-08	0.000000e+00
1.90342e-06   	0.000000e+00	1.704691e-07	9.317723e-07	1.346577e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.477445e-08	0.000000e+00
1.95831e-06   	0.000000e+00	1.664211e-07	8.963859e-07	1.267936e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.428668e-08	0.000000e+00
2.01266e-06   	0.000000e+00	1.626056e-07	8.606177e-07	1.194401e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.382032e-08	0.000000e+00
2.06651e-06   	0.000000e+00	1.590113e-07	8.257931e-07	1.128202e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.338027e-08	0.000000e+00
2.11988e-06   	0.000000e+00	1.556542e-07	7.923155e-07	1.069886e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.297143e-08	0.000000e+00
2.17283e-06   	0.000000e+00	1.525269e-07	7.609180e-07	1.017447e-06	0.000000e+00	0.000000e+00	0.000000e+00	2.259820e-08	0.000000e+00
2.22544e-06   	0.000000e+00	1.496164e-07	7.324782e-07	9.736410e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.226887e-08	0.000000e+00
2.27762e-06   	0.000000e+00	1.465346e-07	7.066297e-07	9.352919e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.191912e-08	0.000000e+00
2.32941e-06   	0.000000e+00	1.434877e-07	6.848880e-07	8.998991e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.158714e-08	0.000000e+00
2.3808e-06    	0.000000e+00	1.405301e-07	6.660989e-07	8.692597e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.126029e-08	0.000000e+00
2.43172e-06   	0.000000e+00	1.375274e-07	6.494031e-07	8.415419e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.091895e-08	0.000000e+00
2.48221e-06   	0.000000e+00	1.347307e-07	6.358199e-07	8.170828e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.059843e-08	0.000000e+00
2.53229e-06   	0.000000e+00	1.321691e-07	6.252074e-07	7.936747e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.029541e-08	0.000000e+00
2.58197e-06   	0.000000e+00	1.297971e-07	6.172238e-07	7.706426e-07	0.000000e+00	0.000000e+00	0.000000e+00	2.000658e-08	0.000000e+00
2.63126e-06   	0.000000e+00	1.275390e-07	6.113378e-07	7.484031e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.972816e-08	0.000000e+00
2.68016e-06   	0.000000e+00	1.253656e-07	6.071383e-07	7.279950e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.945779e-08	0.000000e+00
2.72869e-06   	0.000000e+00	1.232757e-07	6.040237e-07	7.093294e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.919438e-08	0.000000e+00
2.77683e-06   	0.000000e+00	1.212711e-07	6.014336e-07	6.916158e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.893779e-08	0.000000e+00
2.82461e-06   	0.000000e+00	1.193412e-07	5.995559e-07	6.748759e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.868760e-08	0.000000e+00
2.87201e-06   	0.000000e+00	1.174162e-07	5.975158e-07	6.590531e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.843867e-08	0.000000e+00
2.91903e-06   	0.000000e+00	1.155349e-07	5.954072e-07	6.447285e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.819406e-08	0.000000e+00
2.96567e-06   	0.000000e+00	1.137252e-07	5.931181e-07	6.318952e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.795449e-08	0.000000e+00
3.01194e-06   	0.000000e+00	1.120094e-07	5.904828e-07	6.202738e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.772064e-08	0.000000e+00
3.05785e-06   	0.000000e+00	1.104089e-07	5.873203e-07	6.096358e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.749415e-08	0.000000e+00
3.1034e-06    	0.000000e+00	1.089088e-07	5.834934e-07	5.999317e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.727551e-08	0.000000e+00
3.14862e-06   	0.000000e+00	1.075045e-07	5.789331e-07	5.913303e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.706551e-08	0.000000e+00
3.19349e-06   	0.000000e+00	1.061978e-07	5.736304e-07	5.838156e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.686157e-08	0.000000e+00
3.23803e-06   	0.000000e+00	1.049280e-07	5.674663e-07	5.759674e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.665733e-08	0.000000e+00
3.28223e-06   	0.000000e+00	1.037199e-07	5.610776e-07	5.664174e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.646217e-08	0.000000e+00
3.32611e-06   	0.000000e+00	1.026262e-07	5.553960e-07	5.553930e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.627663e-08	0.000000e+00
3.36968e-06   	0.000000e+00	1.015751e-07	5.504035e-07	5.461241e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.609845e-08	0.000000e+00
3.41296e-06   	0.000000e+00	1.005783e-07	5.461918e-07	5.380770e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.592607e-08	0.000000e+00
3.45594e-06   	0.000000e+00	9.962924e-08	5.417998e-07	5.316262e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.575875e-08	0.000000e+00
3.49864e-06   	0.000000e+00	9.868994e-08	5.364300e-07	5.271556e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.559594e-08	0.000000e+00
3.54106e-06   	0.000000e+00	9.775988e-08	5.297018e-07	5.244551e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.543719e-08	0.000000e+00
3.58321e-06   	0.000000e+00	9.685555e-08	5.212361e-07	5.243078e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.528209e-08	0.000000e+00
3.6251e-06    	0.000000e+00	9.599998e-08	5.106776e-07	5.261937e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.513169e-08	0.000000e+00
3.66673e-06   	0.000000e+00	9.522452e-08	4.981649e-07	5.309171e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.498467e-08	0.000000e+00
3.7081e-06    	0.000000e+00	9.447989e-08	4.834693e-07	5.399841e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.484131e-08	0.000000e+00
3.74922e-06   	0.000000e+00	9.373951e-08	4.650713e-07	5.559061e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.470077e-08	0.000000e+00
3.79009e-06   	0.000000e+00	9.302561e-08	4.428461e-07	5.819536e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.456339e-08	0.000000e+00
3.83071e-06   	0.000000e+00	9.230840e-08	4.134616e-07	6.302120e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.442646e-08	0.000000e+00
3.87005e-06   	0.000000e+00	8.938145e-08	3.709697e-07	7.065025e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.393026e-08	0.000000e+00
3.90524e-06   	0.000000e+00	7.964536e-08	2.828025e-07	9.510157e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.239615e-08	0.000000e+00
3.93612e-06   	0.000000e+00	7.408702e-08	3.766166e-07	6.964435e-07	0.000000e+00	0.000000e+00	0.000000e+00	1.131394e-08	0.000000e+00