Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

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.