Problem Statement : In your own words, describe the need for interpolation schemes and flux limiters in FVM. You can use the 1D linear heat conduction equation as an example.                                         …

Problem Statement : Write a code to solve the 1D supersonic nozzle flow equations using the Macormack Method. Implement both the conservative and non-conservative forms of the governing equations Perform grid dependence test Write separate functions for conservative and non-conservative forms Figure out the minimum number…

Our objective was to write a program that solves the following ODE. This ODE represents the equation of motion of a simple pendulum with damping.   In the above equation, g = gravity in m/s2, L = length of the pendulum in m, m = mass of the ball in kg, b=damping coefficient. Wrote a program in MATLAB that simulated…

Objective: Simulating the flow through a backward facing step using multiple meshing schemes and comparing the result among the multiple meshes. Desired Outputs: How does the velocity magnitude profile change as a function of mesh grading factor. Use factors, 0.2, 0.5,0.8 Measure the velocity profile at 0.085 m from the…

Problem Statement: Solving the Steady and Unsteady 2D Heat Conduction equation. 1. Assume that the domain is a unit square.  2. Assume nx = ny [Number of points along the x direction is equal to the number of points along the y direction] 3. Boundary conditions for steady and transient case  …

Problem Statement : To Derive the following 4th order approximations of the second order derivative of the function f(x) = exp(x)*cos(x) 1. Central difference 2. Skewed right sided difference 3. Skewed left sided difference 1. Provide a plot that compares the absolute error between the above mentioned schemes 2. Compare…