How to understand dimensionless data of MacCormack's method

In summary, the individual is conducting a numerical investigation of unsteady heat transfer in a Newtonian fluid within a square cavity. The simulation is solving the governing dimensionless equation using the HSMAC finite difference approach. The fluid flow is being simulated with heating on one vertical side and cooling on the other. The code for the program has been studied and the data has been obtained. However, the data is currently in dimensionless form and the individual is unsure if it needs to be converted to dimensional terms before plotting. They are seeking help with determining the appropriate units and dimensions for the input data and output values.
  • #1
ulfaazmi
17
1
Dear, everyone..

I am doing a numerical investigation of unsteady heat transfer in a Newtonian fluid occupying a square cavity. I solved numerically using HSMAC(Highly Simplified Marker and Cell) finite difference approach as the governing dimensionless equation. The fluid flow is simulated with a heating on vertical side (left) wall and a cooling on vertical side (right) wall. The program has been exist, so I only studied the code of program to get the data and it has been done. but my problem is the data are dimensionless, so need I return those data into dimensional term before drawing??

for example: Vx= nondimensional of velocity in x-axis, and I already got the values.
v = dimensional of velocity in x-axis, where Vx = v/V*
so that in the equation, I defined v = Vx . V*.
where, V*= α/L , α = thermal diffusivity (m2/s), L= Height of enclosure in x-axis (m)

So, need I change the data to get the dimensional parameter as like v,P,T before plotting?? need I change the Vx to v ?
hopefully someone can help me..
thank you.
 
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  • #2
I guess you really want units? So do you know the dimensions (or units) of the input data? What about the governing formula that the code is based on? What would you expect the output to be. Remember that there may be something like Δx or Δt which will be like your step size, but it will carry a dimension.
 

1. What is dimensionless data in MacCormack's method?

Dimensionless data in MacCormack's method refers to the numerical values used in the calculations that are free from any units of measurement. This is achieved by normalizing the data with a characteristic length or time scale. It allows for easier comparison and analysis of results without being affected by the specific units used.

2. Why is it important to understand dimensionless data in MacCormack's method?

Understanding dimensionless data in MacCormack's method is crucial for accurately interpreting and analyzing the results of the calculations. It helps to identify the key factors that affect the outcome and allows for meaningful comparisons between different cases. It also simplifies the equations used in the method and makes it easier to generalize the results.

3. How is dimensionless data calculated in MacCormack's method?

Dimensionless data is calculated by dividing the original numerical values by a characteristic length or time scale that is relevant to the specific problem being studied. This can be a physical length or time, or a parameter that is derived from the problem itself. The resulting values are then used in the calculations, eliminating the units of measurement.

4. What are some common characteristic scales used in MacCormack's method?

Some commonly used characteristic scales in MacCormack's method include the length of the physical domain, the characteristic velocity of the flow, and the characteristic time step used in the calculations. Other parameters such as density, viscosity, and temperature can also be used as characteristic scales depending on the specific problem being studied.

5. How can dimensionless data be interpreted and compared in MacCormack's method?

Dimensionless data can be interpreted and compared in MacCormack's method by looking at the ratios between the values of different variables. For example, if the dimensionless value of a pressure difference is larger for one case compared to another, it can be concluded that the pressure difference is relatively higher in that case. Additionally, plots and graphs of dimensionless data can be used to visually compare and analyze the results.

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