After Break Flashcards
Q: Burgers Equation?
Week:11 [Mid-Sem Break]
Week:12
Lect-26
Q: Burgers Equation?
NS with pressure term drop.
Conservative and Non-conservative formulation (Why) - to better handle shocks & discontinuities as they preserve flux
First-order Upwind scheme, Lax Friedrich (modified FTCS), Lax Wendroff (2nd order in space & time)
Lax wendroff is computationally less economical and their is a method (slight modified) (more economical)
implicit scheme - CN
Q: Implicit scheme for Non-linear equations (eg. 2D Burgers)?
Q: Implicit scheme for Non-linear equations (eg. 2D Burgers)?
implicit schemes are complicated for non-linear terms
generally recommended to treat diffusion terms implicitly (as diffusion is a slow process), while non-linear terms not.
if all terms diffusion + non-linear terms are taken implicitly it will be a very complicated code.
Q: Formulation in different CS [cartesian, cylindrical, spherical]
Lec- 27 Different CS
Q: Formulation in different CS [cartesian, cylindrical, spherical]
reduces the grid size for same no. of points if CS appropriate to geometry
Q: BC at r=0 for cylindrical CS?
Q: BC at r=0 for cylindrical CS?
symmetric BC appropriate since axis of symmetry (dphi/dr)|r=0 = 0
Q: Does GE satisfied at boundary (for cylindrical CS)?
Q: Does GE satisfied at boundary (for cylindrical CS)?
No. Undefined as (0/0)
GE satisfied in limiting sense.
Substituting in GE gives nodal equation at boundary pt.
Q: Why co-ordinate transformation? where mainly used?
Lec: 28
Q: Why co-ordinate transformation? where mainly used?
if not used, then more pts. needed to capture regions of high gradient like BL
grids not aligned with flow
GE doesn’t change it only gets transformed
body in flow domain (like airfoil)
Q: Main difference between Cartesian and Curvilinear co-ordinate system?
Q: Main difference between Cartesian and Curvilinear co-ordinate system?
the unit vectors are global in cartesian CS whereas in curvilinear CS basis vectors are local (tangent to curves)
Q: Choice of Curviliean vs Cartesian?
Q: Choice of Curviliean vs Cartesian?
more computational resources for resolving features or more complicated algorithm & less computational resources.
Q: Formulae for transformation?
Q: Formulae for transformation?
Q: Difference between FDM and FVM?
Lec: 29
Q: Difference between FDM and FVM?
in FDM we solve at discreet points starting point is differential form of GE
in FVM we solve for avg. value of variable over some volum, starting point is integral form
global conservation property of FVM while not for FDM because govering eqn. is enforced at nodes (infinitesmall CV).
FVM is capable of handling complex geometries (as any type of grid can be used) i.e why prefered for industrial applications.
implementation of BC different
Q: Steps of FVM?
Q: Steps of FVM?
integrate the GE
equivalent algebraic system of eqn.
solving the system of eqn.
Lec: 32
Stream Vorticity formulation
Q: How psi-omega? Why? How to obtain primitive variables from Psi-Omega formulation?
Q: How psi-omega? Why? How to obtain primitive variables from Psi-Omega formulation?
Vorticity Evolution equation and Elliptic equation for streamfunction
In primitive variables 3 variables 3 equations, but in psi-omega we have 2 variables and 2 equations (pr. Eliminated which is hard to solve)
Only for 2D flows
Q: Steps for solving Psi-Omega?
Q: Steps for solving Psi-Omega?
Initialize Psi
Find u,v from Psi and omega from u,v
Using VTE for finding new omega and solving Elliptic equation for finding new psi
Update the primitive variables u,v
Lec: 33
Discretizing NS equation
Q: How to discretize N-S equation?
Lec: 33
Discretizing NS equation
Q: How to discretize N-S equation?
Staggered Grid (u,v at cell faces, p at cell centre) [show diagram]
Convective Terms
Discretization of terms will depend which eqn. They are part of i.e x, y or z
Tell difference between 2nd term of x-eqn and 1st term of y-eqn
Diffusion terms
Similar to convective
Q: CFL ? Physical Significance?
Q: CFL ? Physical Significance?
c = u delta t/ delta x <= c_max for 1D
For 3D t_x, t_y and t_z. Min of three
Fluid particle should not travel more than delta x in delta t time step
