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Computational Fluid Dynamics module (CFDM)

CFDM Introduction

Examples showing the class of problems that the code can solve (2-4 examples)


	Brief description of wat the model means, eventually insert link to the benchmark section...or whatever... ADVERTISMENT STYLE no numerical details!!!
	Brief description of what the model means
	Brief description of what the model means
	Brief description of what the model means

Description of the underlying theory and schematic list of the problems this application can solve.

In this application the Navier Stokes equations are solved bla bla..

CFDM Structure

CFDM Fluid types

Incompressible fluid

aaa

Compressible fluid

Constitutive laws

Newtonian
No-Newtonian
- Bingham plastics
- Variable yield model

CFDM Kinematical approaches

Eulerian
- With free surface (level set)
- Without free surface
Lagrangian PFEM (implicitly with free surface)

CFDM Solution strategy

Fractional step
Monolithic

Different solvers are availables (LINK TO SOLVER SECTION!!!!)

In both cases a Newton Raphson residual based strategy is used for linearizing the problem.

CFDM Elements

Linear triangular elements in 2D and linear tetrahedra elements in 3D.

Stabilization techniques availables:

ASGS
OSS

CFDM Boundary conditions

Velocity boundary condition: Inlet of water
Pressure boundary condition: Pressure can be imposed strongly or weakly...
Wall boundary condition:
- Slip/no slip boundary condition
- Wall law
Flag variable?????

CFDM Initial conditions

Initial condition both in velocity and pressure can be set.

CFDM Turbulence models

The user can chose wether to use or not a turbulence model. Those available in kratos are:

Smagorinsky-Lily
Spalart-Allmaras

CFDM HPC

The code can be run in shared or distributed memory:

OpenMP:
MPI:

CFDM Problem parameters

CFDM Others relevand aspects

CFDM Benchmarking

CFDM Tutorials

CFDM Contact people

CFDM Akcnowledgements

Computational Structural Mechanics module (CSMM)

CSMM Introduction

Examples showing the class of problems that the code can solve (2-4 examples)

Description of the underlying theory and schematic list of the problems this application can solve.

The Computational Structural Mechanics module (CSM) is....

CSMM Application Structure

CSMM Analysis Type

The available solutions strategies are:

Static
Dynamic
Relaxed dynamic

With this module you can solve both linear and non linear problems. In case of non linear problems several methods are available:

Newton-Raphson
Newton Raphson with line search
Arch lenght

Different solvers are availables (LINK TO SOLVER SECTION!!!!)

CSMM Elements

Frame Elements:
- Euler-Bernoulli beam short explanation
- Crisfield truss short explanation

2D elements
- Linear triangular element:

Shell elements:
- Isotropic shell: (change the name with the usual one!!!!)
- Ansotropic shell: (change the name with the usual one!!!!)
- EBST shell: (change the name with the usual one!!!!)

Membrane element:

Solid elements:
- Linear tetrahedral element:

Dimension	Element Type	Kratos name	Geometry	Nonlinearity	Material Type
1D	Frame	LinearBeamElement	Line		Isotropic
1D	Truss	CrisfieldTrussElement	Line	Large Displacement	Isotropic
2D	Solid	TotalLagrangian	2D Geometries	Large Displacement	Isotropic
3D	Solid	TotalLagrangian	3D Geometries	Large Displacement	Isotropic
	Shell	ShellIsotropic	3D Triangle	Large Displacement	Isotropic
	Shell	ShellAnisotropic	3D Triangle	Large Displacement	Orthotropic

CSMM Boundary Conditions

Boundary conditions can be set fixing displacements and rotations degrees of freedom.

CSMM Loads

Self weight
Punctual force
Moment
Face pressure (sign convenction!!!!)
Distributed load

CSMM Constitutive laws

The following constitutive laws are available:

Linear elastic:
...

CSMM HPC

The code can be run in shared or distributed memory:

OpenMP:
MPI:

CSMM Problem parameters

...

CSMM Others relevand aspects

...

CSMM Benchmarking

Here validation and verification examples should be inserted

CSMM Tutorials

CSMM Contact people

CSMM Akcnowledgements

Convection Diffusion module (CDM)

CDM Introduction

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes the Convection Diffusion Applications for solving this equation.

Theory

Under the assumption of incompressibility, the governing equations are given by

Problem description

$\rho C \frac{\partial T}{\partial t} + \rho C v \cdot \nabla T + \nabla \cdot q = 0$ (1)

$q = -\kappa \nabla \cdot T$ (2)

In the context of mass difussion within a fluid, (1) is is the mass conservation equation and (2) is a contitutive law proposed by Fourier. The notation is standard: $ρ$ is the density, $C$ the heat capacity, $κ$ the thermal conductivity, $T$ is the temperature, $v$ is the velocity field and $q$ is the diffusive flux per unit fluid density.

Remark: systen can be decoupled since we can plug (2) into (1) and solve the scalar equation

$\rho C \frac{\partial T}{\partial t} + \rho Cv \cdot \nabla T - \nabla \cdot (\kappa \nabla \cdot T) = 0$ (3)

Problem statement

Let us consider the transport by convection and diffusion in an open set $Ω$ $\subset \Re^d$ (d=2 or 3) \ with piecewise smooth boundary $Γ$ , such that $\Gamma = \Gamma_d \cup \Gamma_N$ . The unit outward normal vector to $Γ$ is denoted $n$ . The convection-diffusion initial-boundary value problem can be stated as follows: given a divergence-free velocity field a, the diffusion tensor $κ$ and adequate initial and boundary conditions, find $T$ : $\bar{\Omega} \times \left[ 0, T \left] \rightarrow \Re \right. \right.$ such that

$\rho C \frac{\partial T}{\partial t} + \rho Cv \cdot \nabla T - \nabla \cdot (\kappa \nabla T) = 0 in \Omega \times (0, T)$ (4)

$T (x,0) = T 0 (x) o n Ω$

$T = T_D on \Gamma_D \times (0, T)$

$k (\nabla T) \cdot n = q on \Gamma_N \times (0, T)$

Space discretization method Multiplying Eq.(4) by a test function $W$ and intehrating on the whole domain $Ω$ the equation reads

$\int_\Omega \rho C \frac{\partial T}{\partial t} W d V + \int_\Omega \rho Cv \cdot \nabla T W d V = \int_\Omega (\nabla \cdot (k \nabla T)) W d V$ (5)

Integratin by parts the right term of Eq.(5) leads to

$\int_\Omega \rho C \frac{\partial T}{\partial t} W d V + \int_\Omega v \cdot \nabla T W d V = - \int_\Omega k \nabla T \cdot \nabla W d V$ (6)

Finite element discretization

The temperature is discretized in the standard finite element method manner as $T = \sum N_i T_i$ (7) where $N i$ are the nodal shape functions. Substituting the finite element approximation (7) into the variational equation () and choosing a Galerling formulation ( $W i = N i$ ) leads to the following equation:

$\rho C M \frac{\partial T}{\partial t} + \rho C S T = - \kappa L T$ (7)

Time discretization method Consider a first-order BDF (that is, the Euler implicit scheme)

$\frac{\partial T}{\partial t}=\frac{(T^{n + 1} - T^n)}{\Delta t}$

or a second-order BDF

$\frac{\partial T}{\partial t}= \frac{1}{2} \frac{(3 \times T^{n + 1} - 4 \times T^n + T^{n-1})}{\Delta t}$

CDM Structure

Analysis type

The available solution strategy is:

   Dynamic

With this module you can solve both linear and non linear problems.

CDM Kinematical approaches

Eulerian and Lagrangian approach are available in order to solve the equation.

CDM Solution strategies

CDM Elements

Linear triangular elements in 2D and linear tetrahedra elements in 3D. Both elements are stabilized with OSS.

ConvDiff2D

ConvDiff3D

CDM Boundary conditions

Dirichlet boundary condition:

$T = T_D on \Gamma_D \times (0, T)$

Neumann boundary conditions: $k (\nabla T) \cdot n = q on \Gamma_N \times (0, T)$

CDM Initial conditions

Initial condition in temperature can be set.

CDM HPC

The code can be run in shared or distributed memory:

OpenMP:
MPI:

CDM Problem parameters

The parameters involved in this problem are:

$ρ$ : Density

$C$ :heat capacity

$κ$ : thermal conductivity

$v$ : velocity field

$q$ : diffusive flux per unit fluid density.

$T$ a: ambient temperature.

$σ$ : Stefen Boltzmann constant

e: emissivity

$h$ : convection coefficient

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Contents

Computational Fluid Dynamics module (CFDM)

CFDM Introduction

CFDM Structure

CFDM Fluid types

CFDM Kinematical approaches

CFDM Solution strategy

CFDM Elements

CFDM Boundary conditions

CFDM Initial conditions

CFDM Turbulence models

CFDM HPC

CFDM Problem parameters

CFDM Others relevand aspects

CFDM Benchmarking

CFDM Tutorials

CFDM Contact people

CFDM Akcnowledgements

Computational Structural Mechanics module (CSMM)

CSMM Introduction

CSMM Application Structure

CSMM Analysis Type

CSMM Elements

CSMM Boundary Conditions

CSMM Loads

CSMM Constitutive laws

CSMM HPC

CSMM Problem parameters

CSMM Others relevand aspects

CSMM Benchmarking

CSMM Tutorials

CSMM Contact people

CSMM Akcnowledgements

Convection Diffusion module (CDM)

CDM Introduction

CDM Structure

Analysis type

CDM Kinematical approaches

CDM Solution strategies

CDM Elements

CDM Boundary conditions

CDM Initial conditions

CDM HPC

CDM Problem parameters

CDM Others relevand aspects

CDM Benchmarking

CDM Tutorials

CDM Contact people

CDM Akcnowledgements

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