Convectional numerical methods and deep learning techniques are very relevant and widely used in computational fluid dynamics (CFD) to solve nonlinear differential equations. In this paper, we compare a recently developed cubic spline variation of interpolation technique with the deep learning technique called physics-informed neural networks (PINNs) on the Blasius equation which is a nonlinear differential equation that describes the boundary layer flow of fluids over a flat surface. Both techniques are seen to be comparable with the results from other classical methods where the equation is converted to an initial value problem and then solved.

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Solution of Boundary Layer Blasius Equation by Physics-Informed Neural Networks and Cubic Spline–A Comparison

  • Anamika Devu,
  • S. Swathi Thankam,
  • P. Pramod Nair,
  • Divya Sadasivan

摘要

Convectional numerical methods and deep learning techniques are very relevant and widely used in computational fluid dynamics (CFD) to solve nonlinear differential equations. In this paper, we compare a recently developed cubic spline variation of interpolation technique with the deep learning technique called physics-informed neural networks (PINNs) on the Blasius equation which is a nonlinear differential equation that describes the boundary layer flow of fluids over a flat surface. Both techniques are seen to be comparable with the results from other classical methods where the equation is converted to an initial value problem and then solved.