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Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials.

Martina Bašić1, Branko Blagojević1, Chong Peng2

  • 1Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, Croatia.

Materials (Basel, Switzerland)
|October 23, 2021
PubMed
Summary

Lagrangian Differencing Dynamics (LDD) is a new meshless method for simulating non-Newtonian flows. This robust approach accurately models complex fluid behaviors, offering efficient computation for various applications.

Keywords:
BinghamCassonLDDLagrangianPower Lawmeshlessnon-Newtonianrheology

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Area of Science:

  • Computational Fluid Dynamics
  • Non-Newtonian Fluid Mechanics
  • Numerical Simulation

Background:

  • Accurate simulation of non-Newtonian fluid flows is crucial in many industrial processes.
  • Existing methods often face challenges with computational cost and accuracy for complex flow behaviors.

Purpose of the Study:

  • To introduce a novel meshless and Lagrangian approach, Lagrangian Differencing Dynamics (LDD), for simulating non-Newtonian flows.
  • To demonstrate the robustness and accuracy of the LDD method through benchmark simulations.

Main Methods:

  • Direct discretization and solution of generalized Navier-Stokes equations in strong formulation using second-order-consistent spatial operators.
  • A split-step scheme decoupling pressure and velocity solutions, with pressure solved via a Poisson equation and velocity semi-implicitly.
  • Matrix-free solution and Lagrangian advection of mesh-free nodes enabling parallel CPU and GPU implementation.

Main Results:

  • Validated LDD against four benchmarks, including Abram slump and dam break tests (Bingham model), and lid-driven cavity tests (Casson and Power Law models).
  • Achieved visual and numerical results consistent with experimental data for dam break and slump tests.
  • Demonstrated good agreement with published reports for velocity profiles and streamlines in lid-driven cavity simulations.

Conclusions:

  • The LDD method offers a robust, accurate, and computationally efficient approach for simulating non-Newtonian flows.
  • The method's precise pressure field reproduction allows for future validation of pressure-dependent non-Newtonian models.
  • LDD shows promise for advancing the simulation of complex fluid dynamics with potential for large time steps and parallel implementation.