Pavel
Contents

Convection Diffusion module
Introduction
The numerical solution of convectiondiffusion 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.
Some examples are shown below:
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..
Structure
Fluid types
 Incompressible fluid
aaa
 Compressible fluid
Constitutive laws
 Newtonian
 NoNewtonian
 Bingham plastics
 Variable yield model
Kinematical approaches
 Eulerian
 With free surface (level set)
 Without free surface
 Lagrangian PFEM (implicitly with free surface)
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.
Elements
Linear triangular elements in 2D and linear tetrahedra elements in 3D.
Stabilization techniques availables:
 ASGS
 OSS
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?????
Initial conditions
Initial condition both in velocity and pressure can be set.
Turbulence models
The user can chose wether to use or not a turbulence model. Those available in kratos are:
 SmagorinskyLily
 SpalartAllmaras
HPC
The code can be run in shared or distributed memory:
 OpenMP:
 MPI:
Problem parameters
Others relevand aspects
Benchmarking
Tutorials
Contact people
Akcnowledgements
Computational Structural Mechanics module
Introduction
Examples showing the class of problems that the code can solve (24 examples)
Description of the underlying theory and schematic list of the problems this application can solve.
The Computational Structural Mechanics module (CSM) is....
Application Structure
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:
 NewtonRaphson
 Newton Raphson with line search
 Arch lenght
Different solvers are availables (LINK TO SOLVER SECTION!!!!)
Elements
 Frame Elements:
 EulerBernoulli 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 
Boundary Conditions
Boundary conditions can be set fixing displacements and rotations degrees of freedom.
Loads
 Self weight
 Punctual force
 Moment
 Face pressure (sign convenction!!!!)
 Distributed load
Constitutive laws
The following constitutive laws are available:
 Linear elastic:
 ...
HPC
The code can be run in shared or distributed memory:
 OpenMP:
 MPI:
Problem parameters
...
Others relevand aspects
...
Benchmarking
Here validation and verification examples should be inserted
Tutorials
Contact people
Akcnowledgements
Convection Diffusion module
Introduction
The numerical solution of convectiondiffusion 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
(1)
(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
(3)
Problem statement
Let us consider the transport by convection and diffusion in an open set Ω (d=2 or 3) \ with piecewise smooth boundary Γ, such that . The unit outward normal vector to Γ is denoted n. The convectiondiffusion initialboundary value problem can be stated as follows: given a divergencefree velocity field a, the diffusion tensor κ and adequate initial and boundary conditions, find T : such that
(4)
T(x,0) = T_{0}(x)onΩ
Space discretization method Multiplying Eq.(4) by a test function W and intehrating on the whole domain Ω the equation reads
(5)
Integratin by parts the right term of Eq.(5) leads to
(6)
Finite element discretization
The temperature is discretized in the standard finite element method manner as (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:
(7)
Time discretization method Consider a firstorder BDF (that is, the Euler implicit scheme)
or a secondorder BDF
Structure
Analysis type
The available solution strategy is:
Dynamic
With this module you can solve both linear and non linear problems.
Kinematical approaches
Eulerian and Lagrangian approach are available in order to solve the equation.
Solution strategies
Elements
Linear triangular elements in 2D and linear tetrahedra elements in 3D. Both elements are stabilized with OSS.
ConvDiff2D
ConvDiff3D
Boundary conditions
Dirichlet boundary condition:
Neumann boundary conditions:
Initial conditions
Initial condition in temperature can be set.
HPC
The code can be run in shared or distributed memory:
 OpenMP:
 MPI:
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