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Article

Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

1
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, R. Boškovića 32, 21000 Split, Croatia
2
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; https://doi.org/10.3390/ma14206210
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. https://doi.org/10.3390/ma14206210

AMA Style

Bašić M, Blagojević B, Peng C, Bašić J. Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials. Materials. 2021; 14(20):6210. https://doi.org/10.3390/ma14206210

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. https://doi.org/10.3390/ma14206210

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