Continuum Mechanics

1
Continuum Mechanics
Basic concepts

• On the scale of the object to be studied the
  density and other fluid properties will
  vary smoothly from one point to another
• Gas at normal pressure and low pressure
• Perfect fluid
• Newtonian fluid
• Shear forces are linearly proportional to
  velocity gradients

2
Basic Equations

• Conservation of Mass equation

• Conservation of Momentum

• Steady state equations

3
Simplified General Equations

• Assumptions in order to get simple equations

• Simplified general steady state equation

4
(No Transcript)
5
Galerkin and Weak Formulation

• Relation between test and trial functions

• Orthogonality - Minimum Error

• Definition of Weak formulation
• Advantages

6
Piecewise polynomials and shape functions

• Piecewise polynomial interpolation

• Shape functions

7
Isoparametric Elements

• Four node element

8
Local and Global coordinates

• Shape functions for bilinear isoparametric element

• These shape functions are defined in terms of the
  normalized
• natural domain

9
Mapping from Local to Global
10
Gauss Legendre quadrature

• Function description

• Sampling points
• weighting coefficients
• 2n-1 n

11
Solution to simplified equations
12
Numerical Terminology Formulation

• 201 , 202 , 211 , 222 , 212 , 221

13
Numerical Terminology Formulation
14
Tasks ahead

• Solve Navier stokes with non linear part with
  all possible
• boundary conditions

• To develop numerical solution to Navier Stokes
  equation
• in all coordinate systems