Solving Nav Equation with Mathematica

[mogsy182]

So I am using mathematica to solve the Nav solution equation which is

(Xi - Ux)^2 + (Yi - Uy)^2 + (Zi - Uz)^2 = (ri - Cb)^2

this is what i put in mathematica

NSolve[ {(X1 - U)^2 + (Y1 - V)^2 + (Z1 - W)^2 - (R1 - B)^2 ==
0, (X2 - U)^2 + (Y2 - V)^2 + (Z2 - W)^2 - (R2 - B)^2 ==
0, (X3 - U)^2 + (Y3 - V)^2 + (Z3 - W)^2 - (R3 - B)^2 ==
0, (X4 - U)^2 + (Y4 - V)^2 + (Z4 - W)^2 - (R4 - B)^2 == 0}, {U, V,
W, B}]

and I either get an error or it takes forever to run (ive left it running for ten mins while I am posting this)

anyone knw where I am goin wrong if i am?

 

[mmwave]

Hi there,

It looks like you are trying to use Mathematica to solve a system of equations involving the Navier-Stokes equations. While Mathematica is a powerful tool for solving equations, it may not be the most efficient or appropriate tool for solving complex fluid dynamics equations like the Navier-Stokes equations.

Firstly, the equations you have provided do not seem to be the full Navier-Stokes equations, which are a set of partial differential equations. Instead, they appear to be a simplified version that only includes the velocity components (U, V, W) and pressure (B). This may not give you an accurate solution to your problem.

Additionally, the NSolve function in Mathematica is typically used for finding numerical solutions to algebraic equations, not differential equations. Therefore, it may not be the best tool for solving the Navier-Stokes equations.

I would recommend using a more specialized software or numerical methods specifically designed for solving fluid dynamics equations. Some popular options include ANSYS Fluent, OpenFOAM, and COMSOL Multiphysics. These tools have features and algorithms specifically designed for solving complex fluid dynamics problems and may give you more accurate and efficient solutions.

I hope this helps and good luck with your research!

 

[oswaler]

I am glad to see that you are using a computational tool like Mathematica to solve the Nav equation. This equation is commonly used in fluid mechanics to describe the motion of a fluid in a given space.

From my understanding, the Nav equation is a set of four equations with four unknowns (U, V, W, and B). In your code, you are using the NSolve function to solve the set of equations simultaneously. However, it seems that the code is taking a long time to run or giving you an error.

One potential issue could be the initial values or range of values that you are using for the variables. It is important to choose appropriate values to ensure that the equation can be solved efficiently. You may also want to try using the FindRoot function, which can be more efficient in solving equations with multiple unknowns.

Another potential issue could be the complexity of the equations themselves. If the equations involve high-order terms or multiple variables, it can significantly increase the computational time. In this case, it may be helpful to simplify the equations or break them down into smaller parts to make the computation more manageable.

I would also suggest checking the syntax of your code to ensure that it is correct. It is possible that a small error in the code could be causing the issue.

Overall, it is great that you are using a computational tool to solve the Nav equation. Keep exploring and experimenting with different approaches, and don't hesitate to seek help from other experts or online resources if needed. Good luck!