MATLAB Code Implementation for 3D Vortex Flow Calculation

3D Vortex Flow Calculation and Streamline Visualization

In fluid dynamics and electromagnetic field simulations, 3D vortex flow calculation is commonly used to analyze rotational characteristics of fluids or electromagnetic fields, identifying sources, sinks, and streamline distributions. Implementing this process through MATLAB enables efficient numerical computation and visualization.

Core Implementation Steps Data Preparation Define 3D spatial grid coordinates (X,Y,Z) and corresponding velocity or electromagnetic field vectors (U,V,W). Field data is typically obtained by numerically solving Navier-Stokes equations or Maxwell's equations, or by directly loading experimental/simulation data. In MATLAB, meshgrid() is commonly used to create coordinate arrays, while field data can be imported from CSV files or generated by PDE solvers.

Vortex Characterization Calculation Source and Sink Detection: Determine sources (positive divergence) and sinks (negative divergence) by computing divergence using MATLAB's divergence(X,Y,Z,U,V,W) function, which numerically calculates ∇·V across the vector field. Vorticity Analysis: Curl values reflect vortex intensity. The curl(X,Y,Z,U,V,W) function extracts rotational centers and helps identify vortex structures by computing ∇×V, with magnitude indicating rotation strength.

Streamline Generation and Visualization Streamline Plotting: Based on velocity field data, stream3(X,Y,Z,U,V,W,startx,starty,startz) generates 3D streamlines, while streamline() visualizes them to intuitively display fluid or field paths. Starting positions can be automatically distributed using meshgrid or strategically placed near suspected vortices. Enhanced Representation: Improve readability by adjusting streamline density through start point distribution, applying colormaps (representing velocity or vorticity magnitude), or adding directional arrows using quiver3(X,Y,Z,U,V,W) for vector field representation.

Extended Applications Dynamic Simulation: Incorporate time-series data and create transient vortex evolution animations by looping through streamline updates using animatedline or video writer functions. Parameter Optimization: Compare vortex patterns under different boundary conditions or physical parameters, such as analyzing Reynolds number effects on turbulence through parametric studies and comparative visualizations.

Using MATLAB's built-in vector field analysis and graphics tools enables rapid transition from numerical solutions to scientific visualization, providing intuitive insights for engineering problems. Key advantages include direct handling of 3D data structures, integrated computational functions, and customizable plotting capabilities for professional scientific presentations.