@VamosZhi 请问怎么去掉洞单元和后面的背景单元？paraview做了slice后背景单元的初始自由面总是存在，想把它去掉。

@东岳 OK。谢谢解答！明白了，想成速度是求解变量，想成类似欧拉方程了。常系数，u可以提到外面，可以用形心值，也可以用面上值，都是一样的。用面上的值就可以和密度一起写成通量型式。

@东岳 (2)的积分离散后不应该是 $\left(u_{i} \rho_{i+\frac{1}{2}}-u_{i} \rho_{i-\frac{1}{2}}\right)$ 吗？就是采用体心的速度近似提到积分外面，然后密度梯度的积分才能化为面密度差（积分定理）。

否则，按文中的离散结果，微分项应该是：$ \frac{\partial (rho u)}{\partial x}$, 就是说速度和密度要都在微分号里面才能离散得出（3）的结果。我的疑问就在这里。

http://dyfluid.com/rhocentralfoam.html
（2）中的速度与密度梯度的乘积怎么离散得到（3）中的对应项？
$u \frac{\partial \rho}{\partial x}$ （2）
$\left(u_{i+\frac{1}{2}} \rho_{i+\frac{1}{2}}-u_{i-\frac{1}{2}} \rho_{i-\frac{1}{2}}\right)$ （3）
速度用的是面心得值，如果不用体心的值近似，如何应用高斯定理？

另外，公式（4）中的q应该为$\rho$？

有个skip zero time的选项取消掉应该可以看到0时刻的场。

This is the OpenFOAM language.
http://www.thevisualroom.com/24_openfoam_language/openfoam_language.html

What are features of C++?
What is explicit evaluation?
What is implicit evaluation?
What are the higher level data types?
What are fields?
What are the three types?
What are the five basic classes?
What are the three space-time classes?
What are the three field algebra classes?
What are the two discretisation classes?
What is a geometricField<Type>?
What is the objectRegistry?
What is the IOobject?
How is a dictionary object read?
How is volVectorField read from disk?
How is volScalarField constructed?
What are the read and write options?
How are objects represented in OpenFOAM?
How is matrix inversion done in fvm?
What are lists?
What are fields?
How is memory accessed?
How is IO Communication done?
How are derivatives of fields evaluated?
What are the functions for discretisation?
How can are equations translated into code?
How is the PISO algorithm programmed?
What are header files?
What is wmake?
1.1.1. What are features of C++?
Feature Meaning
typedefs Alias for a possibly complex type name
function Group of statements that perform a task
pointers Data type that holds addresses to refer to values in memory (e.g. for dynamic memory allocation)
data structures Data members grouped under one name (e.g. the nodes in a linked list)
classes Data members and function members grouped under one name
constructor Function member that initialises the instance of it’s class
destructor Function member that destroys the instance of it’s class
friends Allows a function or class access to private or protected members of a class
inheritance Allows a class to be created based on another class (so code can be reused)
virtual member functions Member function that will be redefined in a derived class
abstract class Class that contains at least one virtual function
template Family of classes (class template), functions (function template), variables (variable template) or alias of a family of types (alias template)
namespace Prevents name conflicts in large projects
1.1.2. What is explicit evaluation?
Evaluate spatial derivatives at the current timestep
Uses known values
1.1.3. What is implicit evaluation?
Evaluate spatial derivatives at future timestep
Uses unknown values - generates a matrix equation to be solved
1.1.4. What are the higher level data types?
Type Meaning
volScalarField
scalar, e.g. pressure
volVectorField
vector, e.g. velocity
volTensorField
tensor, e.g. Reynolds Stress
surfaceScalarField
surface scalar, e.g. flux
dimensionedScalar
constant, e.g. viscosity
1.1.5. What are fields?
Arrays of data stored at cell centres in the mesh

Include bouundary information

Three types
volScalarField
volVectorField
volTensorField
Values are stored in named dictionary files in named timestep directories e.g. case/0/p for pressure

1.1.6. What are the three types?
<Type> refers to:

scalar
vector
tensor
1.1.7. What are the five basic classes?
Class Meaning
fvPatchField
(and derived classes)

Boundary conditions
lduMatrix
fvMatrix
(and linear solvers)

Sparse matrices
1.1.8. What are the three space-time classes?
Class Meaning
polyMesh
Stands for polyhedral mesh

Most basic mesh class

Contains:
pointField
faceList
cellList
polyPatchList
fvMesh
Extends polyMesh contains:
Cell volumes (volScalarField)
Cell centres (volVectorField)
Face area vectors (surfaceVectorField)
Face centres (surfaceVectorField)
Face area magnitudes (surfaceScalarField)
Face motion centres (surfaceScalarField)
Time
Class to control time during OpenFOAM
Declared as variable runTime
Provides list of saved times runTime.times()
Timestep = deltaT()
Return current directory name = name()
Time increments = operator++() operator+=(scalar)
Write objects to disk = write()
Start time, end time = startTime(), endTime()
1.1.9. What are the three field algebra classes?
Class Meaning
Field<Type>
Array template class, e.g. Field<vector> = vectorField

Renamed using typedef as:
scalarField
vectorField
tensorField
symmTensorField
tensorThirdField
symmTensorThirdField
dimensionedField

geometricField<Type>
Combination of:
Field
GeometricBoundaryField
fvMesh
dimensionSet
Defines values at all locations in domain with aliases:
volField<Type>
surfaceField<Type>
pointField<Type>
1.1.10. What are the two discretisation classes?
Class Meaning
fvc
Stands for finite volume calculus
Explicit derivative evaluation
Input = known geometricField<Type>
Output = geometricField<Type> object
fvm
Stands for finite volume method
Implicit derivative evaluation
Input = unknown geometricField<Type>
Output = fvMatrix<Type> object, which can be inverted in the matrix equation Mx=y
1.1.11. What is a geometricField<Type>?
volField<Type>
surfaceField<Type>
pointField<Type>
1.1.12. What is the objectRegistry?
Object registry of entities (dictionaries, fields) which are to be read in or written out

1.1.13. What is the IOobject?
Defines I/O attributes of entities managed by the object registry.

1.1.14. How is a dictionary object read?
Code Meaning
Info << "Reading transportProperties" << endl;
Send message to screen
IOdictionary transportProperties
(
IOobject
(
"transportProperties",
runTime.constant(),
mesh,
IOobject::MUST_READ
IOobject::NO_WRITE
)
);
Read in at creation
dimensionedScalar nu
(
transportProperties.lookup("nu")
);
Lookup viscosity in dictionary
1.1.15. How is volVectorField read from disk?
Code Meaning
volVectorField U
(
IOobject
(
"U",
Times[i].name(),
runTime,
IOobject::MUST_READ
),
mesh
)
volVectorField read in from disk
Associated with runTime database
Must be read
1.1.16. How is volScalarField constructed?
Code Meaning
volVectorField magU
(
IOobject
(
"magU",
Times[i].name(),
runTime,
IOobject::NO_READ
IOobject::AUTO_WRITE
),
::mag(U)
);
magU.write();
construct mag(U) object of type volScalarField called magU
write it out
1.1.17. What are the read and write options?
Class Meaning
NO_READ
Object created
MUST_READ
READ_IF_PRESENT
Object asked to read
NO_WRITE
Object destroyed
AUTO_WRITE
Object asked to write
1.1.18. How are objects represented in OpenFOAM?
How to create an object that writes the magnitude of a velocity vector?

Class Meaning
#include "fvCFD.H"
int main(int argc, char argv[])
{

include "addTimeOptions.H"

include "setRootCase.H"

include "createTime.H"

instantList Times = runTime.times();

include "createMesh.H"

One block called main is needed
#include to store commonly used code
runTime is a variable of the OpenFOAM Time class - for timestepping through code
for(label i=0; i<runTime.size(); i++)
{
runTime.setTime(Times[i],i);
Info << "Time: " << runTime.value() << endl
volVectorField U
(
IOobject
(
"U",
Times[i].name(),
runTime,
IOobject::MUST READ
),
mesh
);
Loop over all possible times
Read in a volVectorField U
volScalarField magU
(
IOobject
(
"magU",
Times[i].name(),
runTime,
IOobject::NO READ,
IOobject::AUTO WRITE
),
::mag(U)
);
magU.write();
} return 0;}
Construct a volScalarField magU
Write out the velocity
1.1.19. How is matrix inversion done in fvm?
Each operator in fvm constructs particular entries in known M and y as a fvMatrix object
fvMatrix is a template class (actual classes are fvScalarMatrix etc)
fvMatrix handles storage via lduMatrix class
fvMatrix class also handles solution
1.1.20. What are lists?
Class Meaning
List<Type>
Array template class
Allows creation of a list of any object of a class e.g. List<vector>
PtrList<Type>
List of pointers
SLList<Type>
Non-intrusive singly-linked list
1.1.21. What are fields?
Class Meaning
Field<Type>
Array template class, e.g. Field<vector> = vectorField

Renamed as scalarField, vectorField, tensorField, symmTensorField,
tensorThirdField and symmTensorThirdField

1.1.22. How is memory accessed?
Arrays
Pointers
References
1.1.23. How is IO Communication done?
Code Meaning
Info << "Time = " << runTime.timeName() << nl << endl;
Info object is output to the screen
1.1.24. How are derivatives of fields evaluated?
Time derivative

Divergence (div)
Spatial derivative
Discretised using the flux at the faces
e.g. ∇⋅(uq) (the advection term)
Gradient (grad)
Spatial derivative
e.g. ∇p in the momentum equation
Laplacian
Spatial derivative

Discretised as ∇⋅μ∇q
gradient scheme for ∇q
interpolation for μ
discretisation for ∇⋅
e.g. μ∇2q in the momentum equation

1.1.25. What are the functions for discretisation?
Function Meaning
fvc::ddt(A)
fvm::ddt(A)
Time derivative
∂A/∂t
A can be a scalar, vector or tensor
fvc::ddt(rho,A)
fvm::ddt(rho,A)
Density weighted time derivative
∂ρA/∂t
ρ can be any scalar field
fvc::d2dt2(rho,A)
fvm::d2dt2(rho,A)
Second density weighted time derivative
∂/∂t(ρ∂A/∂t)
fvc::grad(A)
fvm::grad(A)
Gradient
A can be a scalar or a vector
Result is a volVectorField (from scalar) or a volTensorField (from vector)
fvc::div(A)
fvm::div(A)
Divergence
A can be a vector or a tensor
Result is a volScalarField (from vector) or a volVectorField (from tensor)
fvc::laplacian(A)
fvm::laplacian(A)
Laplacian
∇2A
fvc::laplacian(mu, A)
fvm::laplacian(mu, A)
Laplacian
∇⋅(μ∇A)
fvc::curl(A)
fvm::curl(A)
Curl
∇×A
fvm::div(phi,A)
Divergence using flux to evaluate this
A can be a scalar, vector or a tensor
fvm::Sp(rho,A)
Implicit evaulation of source term
fvm::SuSp(rho,A)
Implicit or explicit evaulation of source term (depending on sign of rho
1.1.26. How can are equations translated into code?
Equation Code
∂q∂t+∇⋅qu=μ∇2q
fvScalarMatrix transport
(
fvm::ddt(q)
+ fvm::div(phi,q)
- fvm::laplacian(mu,q)
);

// phi is the flux from the momentum equation
∂T∂t=κ∇2T
solve(fvm::ddt(T) == kappa*fvc::laplacian(T))

// T is a volScalarField defined on the mesh
// A discretised representation of the field variable T
// solve performs matrix inversion for one step
∂k∂t+∇⋅ku−∇⋅[(ν+νt)∇k]=νt[1/2(∇u+∇uT]2−ε/k
solve(
fvm::ddt(k)
+ fvm::div(phi,k)
- fvm::laplacian(nu()+nut,k)
== nut*magSqr(symm(fvc::grad(U)))
- fvm::Sp(epsilon/k,k)
);
1.1.27. How is the PISO algorithm programmed?
The PISO (Pressure Implicit with Splitting of Operators) is an efficient method to solve the Navier-Stokes equations

The algorithm can be summed up as follows:

Set the boundary conditions.
Solve the discretized momentum equation to compute an intermediate velocity field.
Compute the mass fluxes at the cells faces.
Solve the pressure equation.
Correct the mass fluxes at the cell faces.
Correct the velocities on the basis of the new pressure field.
Update the boundary conditions.
Repeat from 3 for the prescribed number of times.
Increase the time step and repeat from 1.
The implementation:

Define the equation for U
fvVectorMatrix UEqn
(
fvm::ddt(U)

• fvm::div(phi, U)

• fvm::laplacian(nu, U)
  );
  Solve the momentum predictor
  solve (UEqn == -fvc::grad(p));
  Calculate the ap coefficient and calculate U
  volScalarField rUA = 1.0/UEqn().A();
  U = rUA*UEqn().H();
  Calculate the flux
  phi = (fvc::interpolate(U) & mesh.Sf())
  • fvc::ddtPhiCorr(rUA, U, phi);
    adjustPhi(phi, U, p);
    Define and solve the pressure equation and repeat for the prescribed number of non-orthogonal corrector steps
    fvScalarMatrix pEqn
    (
    fvm::laplacian(rUA, p) == fvc::div(phi)
    );
    pEqn.setReference(pRefCell, pRefValue);
    pEqn.solve();
    Correct the flux
    if (nonOrth == nNonOrthCorr)
    {
    phi -= pEqn.flux();
    }
    Calculate continuity errors

include "continuityErrs.H"

Perform the momentum corrector step
U -= rUA*fvc::grad(p);
U.correctBoundaryConditions();
The following is from the OpenFOAM UK Users Group:

1.1.28. What are header files?
Sections of code in separate files that are widely used - all function prototypes in a header file

Equation Code
#include "CourantNumber.H"
File containing code for calculating Courant number
1.1.29. What is wmake?
wmake is a make system – directs the compiler to compile specific files in particular ways.

Controlled through files in Make:
files – specifies which user-written files to compile and what to call the result
options – specifies additional header files/libraries to be included in the compilation.

AMD 感觉就像联通，其实在某些方面有很大的优势，常常被低估。

必须支持一下！

每次启动Ubuntu都显示System program problem detected，很烦人，不过修改一个文件就可以。

执行命令：

sudo gedit /etc/default/apport

将enabled=1改为enabled=0保存退出即可

senn1=(Ua&U); 你确保&前后都有空格吗？