Solution of 2-D Incompressible Navier Stokes Equations with Artificial Compressibility Method Using Ftcs Scheme

Submission: The report from part 4 including all relevant graphs and numerical analysis along with interpretations.

We calculated the number of iterations $\tau$ needed to achieve $|f^{\tau}(x) - f^{\tau}({x^\prime})| > 10^{-1}$ when given two initial conditions $x_0$ and $x^{\prime} =x_0 + \epsilon$ separated apart $\epsilon = 10^{-d}$. Here, the exponent $d$ represents the number of digits of precision $d = \lfloor \log |x_0 - x^{\prime}| \rfloor$. Fig.~\ref{fig:precisiondelta} depicts a log-log plot of data obtained from several average random initial conditions and its initial distance $\epsilon$ for different digits precision $d=\{10, 20, \ldots, 290\}$.

by the Trapezoidal rule is Etrap = O(h2 ) and by Simpson’s rule is ESimp = O(h4 ). i) For each of these numerical integration rules, what conditions are required on the integrand f so these error estimates are valid? ii) Suppose that the error using h = 5 × 10−3 is E0 = 1.19 × 10−4 when using either the Trapezoidal rule or Simpson’s rule. For both rules, ˆ estimate the error if an interval width of h = 1 × 10−3 is used. iii) The Matlab command [z, w] = gauleg(N); calculates the N Gauss-Legendre nodes z and weights w for the interval [−1, 1]. Show how z and w can be used to numerically calculate

First, The procedures of were take an energy car and roll it down a track with a without a sail and record the data from photogate A to B and the time to took to get there make sure the photogate are 555 cm away from each other. Do the same one energy car wit just wheels and one with one 3 times each.

© The Authors JCSCR. (2012). A Comparative Study on the Performance. LACSC – Lebanese Association for Computational Sciences Registered under No. 957, 2011, Beirut, Lebanon, 1-12.

seem to change in the same way. Then, go back to get the initial velocities the same, and

1) Once the simulation opens, click on ‘Show Both’ for Velocity and Acceleration at the top of the page. Now click and drag the red ball around the screen. Make 3 observations about the blue and green arrows (also called vectors) as you drag the ball around.

The remaining results used to obtain the graph in the next section can be obtained by, iteratively substituting the parameters shown in table 3 below for the various architectures and various population sizes. The system parameters given in [16] is shown in table 3.

From the first test, which had the dummies sitting upright, and the data was: 41ft/sec, 54 milisec collision time, and 21g-force exerted on the

INSTRUCTIONS: Read the references found on the Background Info page. Study the examples there, and the ones given below. Work out the problems, showing all the computational steps. This is particularly important for those problems for which the answers are given. On those problems, the correct procedure is the only thing that counts toward the assignment grade.

The model is set to the angle of 4.1 degrees and the 30 readings from the multitube manometer, which are connected to points on the aerofoil surface, are measured and recorded. Along with these readings the two tubes connected to the tunnel reference pressure tappings are recorded. These steps are repeated but with an angle of attack of 6.1 degrees. It was found from the experiment that the stall angle was around 8.8 degrees. This was found by increasing the angle of attack until the

Providing a proper equation of state for each phase has a crucial role in the numerical simulation of compressible liquid-vapor two-phase flows. Furthermore, these equations of state are required to be thermodynamically consistent, computationally cost effective and as accurate as possible, however, determining the constant parameters in these equations for any fluid type should not be cumbersome. In this paper, an equation of state is obtained for the liquid phase by Taylor expansion of internal energy about a reference point. By employing thermodynamic relations, other thermodynamic properties such as enthalpy, entropy and Gibbs function are obtained. Subsequently, this equation of state for the liquid phase is associated with a stiffened gas equation of state for the vapor phase which is proven to have a acceptable accuracy for the gases.

11. Change the y velocity of the blue planet (body 3) to 90 and the green planet (body 4) to 70.

Q6b. Write down the simplified Cartesian Navier-Stokes momentum equations that you think are the closest representation to the equations you actually solved in Fluent. State why these aren’t actually the equations you solved. (10 marks)

-The Reynolds number of this experiment was then calculated using equation (4) where c is the length of the aerofoil chord and is the dynamic viscosity of air.