Linear convection equation solver

 How does an unstable solution look like? If the error obtained at one time step of the calculation causes the errors to be magnified as the computations are continued, then the solution is said to be unstable.  If the error eventually die out without any further magnification, then the solution is said to be…

1. Fastest steady state solution is obtained by the SOR iterative method with less no.of ietrations and less simulation time. It took 31 iterations with 0.101s simulation time to solve 2D heat conduction equation with the given initial & boundary conditions.    The optimum value of the relaxation…

  AIM: To solve 2D heat conduction equation using steady and unsteady solvers with different iterative techniques   ASSUMPTIONS: 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]…

The objective of this project is to write a Matlab/Octave program that solves the following equation and Simulate the motion between 0-20 sec                                          In the above equation, g =…

Even though exact analytical solutions are available for quasi 1D nozzle flow problems, why do we strive hard to compute the non-exact numerical solution?        OBJECTIVE - To answer the above question, we should first observe the objective of this project. The primary goal of this project is…

Link to the simulation video: Shock tube simulation video Objective: To understand the working of Shock Tube To understand the concept of 'Events' in the Converge Studio Shock Tube setup and working:        The shock tube is a simple duct closed at both ends. A diaphragm divides this duct into…

Assumptions made to solve the Linear Convection equation Domain length is L = 1m The initial velocity profile is a step function. It is equal to 2m/s between x= 0.1 and 0.3 and 1m/s everywhere else First order forward differencing for the time derivative First order backward/rearward differencing for the space term. Time…

  AIM: To solve 2D heat conduction equation using steady and unsteady solvers with different iterative techniques   ASSUMPTIONS: 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]…

Fourth order approximations of the second order derivative using the following schemes are derived with the help of Programming Central difference Skewed right sided difference Skewed left sided difference Wrote a Matlab program to evaluate the second order derivative of the analytical function exp(x)*cos(x) and compared…

Objective: To understand the theory of formation of expansion fan due to infinite mach waves, originated at the sharp convex corner   To understand the reason for the usage of Neumann BC at the outlet for supersonic flow To understand the effect of SGS parameter on shock location To understand the effect of using…

OBJECTIVE OF THIS PROJECT IS THE UNDERSTAND THE FOLLOWING : CHT simulation is used to simultaneously predict the heat transfer in the fluid and the solid portions of the domain. In fluid heat transfer takes place faster when compared to solids, therefore to overcome this issue fluid solver is made to freeze periodically…

1. Transient flow simulation of fluid over a throttle body is carried out using transient solver. No hydrodynamic mode can be used to check whether the mesh generation process is taking place correctly  2. Reynolds Averaged Navier-Stokes method is used to solve the compressible fluid flow inside the bent pipe and RNG-K…

1. Steady state flow simulation of fluid over a throttle body is carried out using Pressure-based steady solver  2. Reynolds Averaged Navier-Stokes method is used to solve the compressible fluid flow inside the bent pipe and RNG-K epsilon turbulence model is chosen  3. Fixed embedding option is enabled in…

1. Backward step geometry is drawn in the converge studio. Dimensions are determined from the file provided by the skill lync. 2. Three different base mesh sizes are used (Converge studio resulted that the order of 10^-4 is too small and could result in data overflow, so the following values are chosen) 2e-3m 1.5e-3m 1e-3m…

1. Channel flow case is set, with the help of tutorial videos provided by convergent science. 2. Three different base mesh sizes are used 2e-4m 1.5e-4m 1.2e-4m 3. Cygwin is used to run the simulation and in the converge studio the binary outputs are post processed to the format that Paraview can read. 4. Line probe is…

The main objective of this project is to simulate the flow through a backward facing step using icoFoam solver, with multiple meshes. But as an extensive study, flow through the backward facing step is simulated using two solvers, in this project. My primary intention was to complete the objective of…

 How does an unstable solution look like? If the error obtained at one time step of the calculation causes the errors to be magnified as the computations are continued, then the solution is said to be unstable.  If the error eventually die out without any further magnification, then the solution is said to be…

1. Fastest steady state solution is obtained by the SOR iterative method with less no.of ietrations and less simulation time. It took 31 iterations with 0.101s simulation time to solve 2D heat conduction equation with the given initial & boundary conditions.    The optimum value of the relaxation…