scholarly journals Dewetting dynamics of anisotropic particles: A level set numerical approach

2021 ◽  
pp. 1-29
Author(s):  
Siddharth Gavhale ◽  
Karel Švadlenka
Keyword(s):  
Level Set ◽  
Numerical Approach ◽  
Anisotropic Particles

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

2015 ◽  
Vol 18 (1) ◽  
pp. 203-229 ◽  
Author(s):  
Guoqiao You ◽  
Shingyu Leung
Keyword(s):  
Dynamical Systems ◽  
Level Set Method ◽  
Level Set ◽  
Limit Cycles ◽  
Time Discretization ◽  
Numerical Approach ◽  
Initial Guess ◽  
Implicit Time ◽  
Time Step ◽  
Image Regularization

AbstractWe propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions. Since the derivation is based on a semi-implicit time discretization, this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method. As an interesting application of the numerical approach, we propose a new variational approach for extracting limit cycles in dynamical systems. The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles. Further, we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

scholarly journals Modelling dynamic ice-sheet boundaries and grounding line migration using the level set method

2020 ◽  
Vol 66 (259) ◽  
pp. 766-776
Author(s):  
M. Alamgir Hossain ◽  
Sam Pimentel ◽  
John M. Stockie
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Numerical Approach ◽  
Ice Surface ◽  
Grounding Line ◽  
High Degree ◽  
Ice Water ◽  
Benchmark Solutions

AbstractComputing predictions of future sea level that include well-defined uncertainty bounds requires models that are capable of robustly simulating the evolution of ice sheets and glaciers. Ice flow behaviour is known to be sensitive to the location and geometry of dynamic ice boundaries such as the grounding line (GRL), terminus position and ice surface elevation, so that any such model should track these interfaces with a high degree of accuracy. To address this challenge, we implement a numerical approach that uses the level-set method (LSM) that accurately models the evolution of the ice–air and ice–water interface as well as capturing topological changes in ice-sheet geometry. This approach is evaluated by comparing simulations of grounded and marine-terminating ice sheets to various analytical and numerical benchmark solutions. A particular advantage of the LSM is its ability to explicitly track the moving margin and GRL while using a fixed grid finite-difference scheme. Our results demonstrate that the LSM is an accurate and robust approach for tracking the ice surface interface and terminus for advancing and retreating ice sheets, including the transient marine ice-sheet interface and GRL positions.

scholarly journals A numerical approach for non-Newtonian two-phase flows using a conservative level-set method

2020 ◽  
Vol 385 ◽  
pp. 123896 ◽  
Author(s):  
Ahmad Amani ◽  
Néstor Balcázar ◽  
Alireza Naseri ◽  
Joaquim Rigola
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Numerical Approach ◽  
Two Phase Flows ◽  
Two Phase ◽  
Conservative Level Set

Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis

2014 ◽  
Vol 33 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Piotr Putek ◽  
Piotr Paplicki ◽  
Ryszard Pałka
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Permanent Magnet ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Approach ◽  
Design Sensitivity ◽  
Optimization Process ◽  
Content Type ◽  
Rotor Poles

Purpose – In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose the modified multi-level set method (MLSM) was proposed and applied to capture the shape of rotor poles on the fixed mesh using FE analysis. The paper aims to discuss these issues. Design/methodology/approach – This framework is based on theories of topological and shape derivative for the magnetostatic system. During the iterative optimization process, the shape of rotor poles and its evolution is represented by the level sets of a continuous level set function f. The shape optimization of the iron and the magnet rotor poles is provided by the combining continuum design sensitivity analysis with level set method. Findings – To obtain an innovative design of the rotor poles composed of different materials, the modified MLSM is proposed. An essential advantage of the proposed method is its ability to handle a topology change on a fixed mesh by the nucleating a small hole in design domain that leads to more efficient computational scheme then standard level set method. Research limitations/implications – The proposed numerical approach to the topology design of the 3D model of a PM machine is based on the simplified 2D model under assumption that the eddy currents in both the magnet and iron parts are neglected. Originality/value – The novel aspect of the proposed method is the incorporation of the Total Variation regularization in the MLSM, which distribution is additionally modified by the gradient derivative information, in order to stabilize the optimization process and penalize oscillations without smoothing edges.

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