What is the SIMPLE Algorithm?
- It obtains a velocity field by solving the momentum equations ( Doesnt satisfy continuity eq.)
- Solve Possion eq to get the pressure field
- Use the pressure field to correct velocity field in contiuity eq
- new velocity field doesnt satisfy momentum eq -> repeat cycle
What is the purpose of finite volume methods?
Subdivision of domain into discrete elements
What is the purpose of Spatial Discretization
Approximation of Spatial Gradients
What is the purpose of Temporal Discretization?
Evolution of physical state variables in time
How do Finite Volume Methods Work?
- Equations Discretized using a generic 3D polyhedral cell
- Flow variables calculated at cell centroid
- Incorporate neighbor cells
- Integrate Navier Stokes Equations across the cell
- Use different approach based on Complexity of Equation
What is implicit treatment?
Adding linear source term to M matrix
What is explicit treatment?
Adding linear source term to b vector
How do you deal with the convection term in FVM?
Use divergence theorem or Gauss and convert volume integral to surface integral
What is non-orthogonality in CFD?
Shared faces have a face angle
Why are the Naver Stokes Equations difficult to solve numerically?
- No equation for p, only for velocity components
- The computed velocity fields from the momentum equations must satisfy the continuity equations
- The convection term in the momentum equation is non linear
- We cant use equation of state to compute pressure because density and temperature may be constant
How do we solve the pressure velocity coupling problem for Steady incompressible Navier Stokes equations?
-SIMPLE Algorithm
- Convert the equations into matrix form Mu = - /nabla p where M are the coefficients, p is the pressure and u is the velocity
What are five important terms in the momentum equation?
- Temporal derivative
- Convection
- Pressure gradient
- Diffusion term
- Source Term
What is the formula for the matrix form of NSE?
Mu = -\nabla p
How are constant source terms like gravity handled in the SIMPLE algorythm?
Append them to the b vector
How do you solve the SIMPLE algorythm?
- Solve momentum equation for velocity field
- Solve Poisson equation for pressure field
- Use pressure field to correct velocity field so it satisfies continuity equation
- The velocity field now does not satisfy momentum equation so iterate
