Interpolation definition:
In the numerical analysis, interpolation is a method of
constructing new data pointswithin the range of a discrete
set of known data points .
Linear Interpolation:
In Mathematics linesr interpolation is a method of curve fitting
using linear polynomials to construct new data points within the
range of a discrete set of known data points.
Upwind schemes:
upwind schemes is a class of numerical discretization methods
for solving hyperbolic partial differential equations.
Upwind schemes use a solution-sensitive finite difference
stencil to numerically simulate the direction of propagation
of information in a flow field. The upwind schemes attempt to
discretize hyperbolic partial differential equations.
Quick scheme:
In computational fluid dynamics QUICK,
which stands for Quadratic Upstream Interpolation for
Convective Kinematics, is a higher-order differencing
scheme that considers a three-point upstream weighted
quadratic interpolation for the cell value
In order to find the cell face value a quadratic function passing through
surrounding nodes and one node on the upstream side must be used.
In central differencing scheme and second order upwind scheme the first order derivative is included and the second order derivative is ignored.
Flux limiter:Flux limiter and slope limiter are basically same thing slope limiter is used to limit the system state whereas flux limiter is use to limit the fluxes mathematical significance of slope and flux limiters is same they both limit the solution when shock or discontinuety is observe
The main idea behind the construction of flux limiter schemes is to limit the spatial derivatives to realistic values for engineering problems this usually means physically realiable and meaningful values. They are used in high resolution schemes for solving problems
The idea behind construction of high resolution scheme is to limit the discontinuity in high order and low order numerical scheme using flux limiters in such a way that numerical solution gives the high order accuracy
F(j+1/2)=L(j+1/2)+phi(H(j+1)2-L(j+1/2))
L,H are flux of conservative low and high order scheme
Phi= function of smoothness