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A Novel Lagrangian Gradient Smoothing Method for Fluids and Flowing Solids

Mao, Zirui
http://orcid.org/0000-0003-3223-8921
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553252214052311

Abstract Details

2019, PhD, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian meshfree method by solving Navier-Stokes differential governing equations. With the key features of `Lagrangian’ and `meshfree’, SPH has huge advantages in tracking the free interfaces and handling large deformation. However, SPH was born with a series instability problem when particles are subjected to tension, known as the `tensile instability’. Although the instability issue can be treated completely by adopting some ad-hoc correction techniques, these additional techniques would either affect the accuracy of numerical solution or lead to a much more complicated implementation procedure. Considering that the tensile instability problem is highly related to the loose connecting mechanism of SPH particles, in this work, a SPH-like Lagrangian meshfree method, named as Lagrangian Gradient Smoothing Method or L-GSM, is proposed by replacing the SPH gradient technique with a more rigid GSM gradient operator in order to avoid the `tensile instability’ problem. The replacement of the gradient approximation technique requires a series of special treatments different from the existing SPH method in the aspects of particle-searching algorithm, supporting domain-construction algorithm, free surface with particles deficiency, boundary treatments, and how to guarantee the rigid conservation of flow in simulation. For the searching algorithm of neighboring particles, a global searching algorithm based on Delaunay triangulation and a novel local neighbor-searching (LNS) algorithm are proposed in this work for the L-GSM framework. Particularly, the newly proposed LNS algorithm can greatly enhance the computational efficiency of L-GSM and provide LL-GSM (Local L-GSM) a huge advantage over SPH in computational efficiency. For the construction of supporting domain, a 3D localized domain-constructing algorithm is developed effectively for the 3D L-GSM. To mimic the free surface effect accurately, I derived three types of correction techniques through i) assigning virtual particles beyond the free surface, ii) deducting the normalized form for the standard GSM gradient operator, and iii) deducting the consistent form for the discretized governing equations. Moreover, a stable and desirable solid boundary is also designed in this study for L-GSM framework. To ensure the conservation of flow, a conservatized form of governing equations is deducted, by which the conservation rule can be held even in the `remeshing’ (updating of neighboring particles) process. Then, the accuracy, stability and computational efficiency of the proposed L-GSM/LL-GSM framework are investigated comprehensively by conducting some theoretical analysis and numerical experiments. Finally, the L-GSM/LL-GSM model is validated by a series of applications in hydrodynamics and granular flows through comparing the L-GSM/LL-GSM solutions with the corresponding theoretical solutions, experimental results and other numerical solutions. Results show that the proposed L-GSM/LL-GSM framework can always generate an accurate numerical solution to large deformation problems in hydrodynamics and granular flows without the existence of the `tensile instability’ issue in both 2D and 3D. In addition, both L-GSM and LL-GSM own a superior computational efficiency than SPH under the same conditions, especially the LL-GSM scheme associated with the highly efficient LNS algorithm.
Gui-Rong Liu, Ph.D. (Committee Chair)
Shaaban Abdallah, Ph.D. (Committee Member)
Mark Turner, Sc.D. (Committee Member)
195 p.
Geotechnology
Lagrangian Gradient Smoothing Method; Meshfree method; large deformation; Free surface flows; Hydrodynamics; Granular flows

Recommended Citations

Citations

  • Mao, Z. (2019). A Novel Lagrangian Gradient Smoothing Method for Fluids and Flowing Solids [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553252214052311

    APA Style (7th edition)

  • Mao, Zirui. A Novel Lagrangian Gradient Smoothing Method for Fluids and Flowing Solids. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553252214052311.

    MLA Style (8th edition)

  • Mao, Zirui. "A Novel Lagrangian Gradient Smoothing Method for Fluids and Flowing Solids." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553252214052311

    Chicago Manual of Style (17th edition)

ucin1553252214052311
276
© 2019, some rights reserved.Creative Commons License A Novel Lagrangian Gradient Smoothing Method for Fluids and Flowing Solids by Zirui Mao is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.