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Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, Croatia
Institute of Geotechnical Engineering, University of Natural Resources and Life Sciences Vienna, Feistmantelstraße 4, 1180 Wien, Austria
Author to whom correspondence should be addressed.
Academic Editor: Antonio Lamura
Materials 2021, 14(20), 6210;
Received: 25 August 2021 / Revised: 11 October 2021 / Accepted: 11 October 2021 / Published: 19 October 2021
This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated. View Full-Text
Keywords: non-Newtonian; rheology; Lagrangian; meshless; LDD; Casson; Bingham; Power Law non-Newtonian; rheology; Lagrangian; meshless; LDD; Casson; Bingham; Power Law
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MDPI and ACS Style

Bašić, M.; Blagojević, B.; Peng, C.; Bašić, J. Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials. Materials 2021, 14, 6210.

AMA Style

Bašić M, Blagojević B, Peng C, Bašić J. Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials. Materials. 2021; 14(20):6210.

Chicago/Turabian Style

Bašić, Martina, Branko Blagojević, Chong Peng, and Josip Bašić. 2021. "Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials" Materials 14, no. 20: 6210.

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