Derivation  of 4th order approximation of second order derivative 1. Central Difference apprx  `(del^2f)/(delx^2) = af(i-2) +bf(i-1)+cf(i)+df(i+1)+ef(i+2)`   `f(i)` `Deltaxf'(i)` `Deltax^2f''(i)` `Deltax^3f'''(i)` `Deltax^4f''''(i)` `af(i-2)` `a` `-2a` `(4a)/2` `-(8a)/6` `(16a)/24` `bf(i-1)` `b` `-b` `b/2`…

The 2D conduction equation  `(delT)/(delt) = alpha((del^2T)/(delx^2) + (del^2T)/(dely^2))` where `alpha` is the thermal diffusivity of material  In Steady state flow the temperature does not change with time. Therefore the time derivative term is neglected  `((del^2T)/(delx^2) + (del^2T)/(dely^2)) = 0` The…

OBJECTIVE: To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle and  derive both the conservation and non-conservation forms of the governing equations and sovle them using the MacCormack's technique. Assumptions Made: 1. The flow is steady, isentropic through a convergent-divergent nozzle  2.…

BlockMesh Drill down Challenge: Objective : To simulate an incompressible-laminar-viscous flow through the backward facing step geometry. Case 1 - Simulate the flow without using any grading factor (i.e., GF = 1) Case 2 - Simulate the flow with grading factor of 0.2. The cells should be finer near the walls (includig the…

Finite Volume Method The Finite Volume Method (FVM) is a discretization method for the approximation of a single or a system of partial differential equations expressing the conservation, or balance, of one or more quantities. As in the finite element method, a mesh is constructed, which consists…

Objective : To Simulate the incomressible laminar flow through a pipe using OpenFoam Validate Hydro-dynamic length with the numerical result Validate the fully developed flow velocity profile with its analytical profile Validate maximum velocity and pressured drop for fully developed flow Post-process Shear stress and…

Objective : To Simulate the incomressible laminar flow through a pipe using OpenFoam   Validate Hydro-dynamic length with the numerical result Validate the fully developed flow velocity profile with its analytical profile Validate maximum velocity and pressured drop for fully developed flow Post-process Shear…