AIM: To generate a plot comparing the different schemes such as the central differencing, left-skewed, and right-skewed schemes for deriving 4th order approximation of a 2nd order derivative using the Taylor Table method.   GIVEN DATA: `f(x) = e^x.cos(x)` Analytical solution: `f''(x) = -2e^xsin(x)`   The expression…

AIM: To solve the 2D heat conduction equation by using the point iterative techniques for both steady state and transient cases   METHODS FOLLOWED: Considering the following grid and grid points for the 2D heat conduction problem where T represents temperature at the respective points This equally spaced grid…

AIM: To simulate the 1D supersonic nozzle flow through a convergent-divergent nozzle using the Macormack method. THEORY: A convergent-divergent nozzle is a type of nozzle that is used to generate supersonic flow speed conditions from the subsonic inlet conditions. This occurs as a phenomenon of the convergent portion…

Aim: To simulate an incompressible-laminar-viscous flow through the backward-facing step geometry. Given data: The geometry dimensions and domain specifications Mesh specification Number of cells along the x-direction = 200 Number of cells along the y-direction = 20 Two cases will be simulated one with a grading factor…

Finite Volume Method (FVM) solves the governing equations that describe the flow over a volume instead of a point, irrespective of the shape of the volume which provides an advantage of formulating and working with unstructured meshes in comparison to the finite difference method (FDM). The flow quantities are conserved…

AIM: To simulate an axisymmetric flow by applying the wedge boundary condition through a pipe in OpenFOAM GIVEN DATA: Flow properties that are considered for simulation obey the Hagen-Poisuelle flow equation. The flow is laminar, incompressible, along the length of the pipe, and flows through a constant cross-section…

Aim: Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation for flow along a pipe using OpenFOAM.   Given data: Flow properties that are considered for simulation obey the Hagen-Poisuelle flow equation. The flow is laminar, incompressible, along the length of the pipe, and flows through…