New Mesh Relaxation Technique in Multi-Material ALE Applications

2004 ◽  
Author(s):  
K. Mahmadi ◽  
N. Aquelet ◽  
M. Souli
Keyword(s):  
High Pressures ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Relaxation Parameter ◽  
Numerical Results ◽  
Arbitrary Lagrangian Eulerian ◽  
Fine Mesh ◽  
Transient Problems ◽  
Control Mesh ◽  
Shock Fronts

The Arbitrary Lagrangian-Eulerian (ALE) method is a method that contains both pure Lagrangian and pure Eulerian formulations. It is assumed to be capable to control mesh geometry independently from material geometry. However for transient problems involving pressure wave, this method will not allow to maintain a fine mesh in the vicinity of the shock wave for accurate solution. A new mesh relaxation method for explicit multi-material arbitrary Lagrangian Eulerian finite element simulations has been developed to keep an as “Lagrange like” fluid mesh as possible as in the vicinity of shock fronts, while at the same time keeping the mesh distortions on an acceptable level. However, the relaxation parameter must be defined for general applications of high pressures, it is the objective of this work. In this paper we present numerical results of three shock waves problems. For every application, numerical results will be compared with the experimental results in order to improve to understanding how the relaxation parameter is chosen.

A Conservative Iterative-Based Zonal Decomposition Scheme for Conduction Heat Transfer Problems

1999 ◽  
Vol 121 (1) ◽  
pp. 169-173 ◽  
Author(s):  
O. E. Ruiz ◽  
W. Z. Black
Keyword(s):  
Finite Difference ◽  
Numerical Technique ◽  
Accurate Solution ◽  
Relaxation Parameter ◽  
Decomposition Technique ◽  
Rapid Convergence ◽  
Conduction Heat Transfer ◽  
Decomposition Scheme ◽  
Transient Problems ◽  
Transfer Problems

A new conservative iterative-based zonal decomposition technique for the solution of complex heat conduction problems is proposed. This numerical technique is based on dividing the domain into subdomains and ensuring that the heat flux and temperature are continuous at the boundary between subdomains. An example problem is used to illustrate the zonal decomposition technique for both steady and transient problems. This numerical technique results in accuracy which equals or exceeds traditional finite difference solutions and solution times which are significantly less than traditional finite difference solutions. A numerical relaxation parameter is introduced and its value is optimized to provide the most rapid convergence to an accurate solution.

Analysis of Twisting Stiffness for a Multifiber Composite Layer

1974 ◽  
Vol 41 (3) ◽  
pp. 658-662 ◽  
Author(s):  
C. W. Bert ◽  
S. Chang
Keyword(s):  
Cross Section ◽  
Least Squares Method ◽  
Rectangular Cross Section ◽  
Torsional Rigidity ◽  
Composite Layer ◽  
Circular Cross Section ◽  
Relaxation Method ◽  
Fiber Composites ◽  
Numerical Results ◽  
Torsion Problem

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

scholarly journals Optimal multistage relaxation with automatic parameter selection

2021 ◽  
Author(s):  
Alvin Wong
Keyword(s):  
Fourier Series ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Convergence Time ◽  
Fourier Series Expansion ◽  
End User ◽  
Local Flow ◽  
Flow Problems ◽  
User Expertise ◽  
Complex Fourier Series

This research developed a numerical method that solves complicated fluid flow problems without requiring end-user expertise with the solver. This method is capable of obtaining a spatially accurate solution in the same time or better as a skilled user with a conventional solver. An explicit preconditioned multigrid solver was used in this research with a multistage relaxation method. The prosposed method utilizies a database with optimized relaxation method parameters for different local flow and mesh conditions. The parameters are optimized for the relaxation such that the error modes in a complex Fourier series expansion of the residual can be quickly reduced. The convergence time and iteration count of this method was compared against the same solver using default input values, as well as a pre-optimized solver, to simulate a skilled user for various geometries. Improvements in both comparisons were demonstrated.

scholarly journals Optimal multistage relaxation with automatic parameter selection

2021 ◽  
Author(s):  
Alvin Wong
Keyword(s):  
Fourier Series ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Convergence Time ◽  
Fourier Series Expansion ◽  
End User ◽  
Local Flow ◽  
Flow Problems ◽  
User Expertise ◽  
Complex Fourier Series

This research developed a numerical method that solves complicated fluid flow problems without requiring end-user expertise with the solver. This method is capable of obtaining a spatially accurate solution in the same time or better as a skilled user with a conventional solver. An explicit preconditioned multigrid solver was used in this research with a multistage relaxation method. The prosposed method utilizies a database with optimized relaxation method parameters for different local flow and mesh conditions. The parameters are optimized for the relaxation such that the error modes in a complex Fourier series expansion of the residual can be quickly reduced. The convergence time and iteration count of this method was compared against the same solver using default input values, as well as a pre-optimized solver, to simulate a skilled user for various geometries. Improvements in both comparisons were demonstrated.

Analysis of the characteristics of air–yarn coupling movement in the profiled reed groove of an air-jet loom

2021 ◽  
pp. 004051752110569
Author(s):  
Yuzhen Jin ◽  
Hailang Xiong ◽  
Jingyu Cui
Keyword(s):  
Numerical Results ◽  
Weft Yarn ◽  
Valuable Insight ◽  
Arbitrary Lagrangian Eulerian ◽  
Air Jet ◽  
Gap Ratio ◽  
Gas Consumption ◽  
Simulation Results ◽  
Gas Leaks ◽  
Air Jet Loom

The movement characteristics of yarn in the profiled reed groove of an air-jet loom can have a great impact on the performance of the fabric. Unstable yarn movement tends to lead to weft defects, as short wefts or weft breaks may occur, which could deteriorate the quality of the final fabric. In this paper, the characteristics of the yarn movement in a profiled reed groove are numerically studied. The arbitrary Lagrangian–Eulerian method is used to solve the two-way airflow–yarn interaction and the yarn is simulated with the ball–socket model. A fluctuation ratio is defined to characterize the unsteadiness of the yarn movement. Our simulation first investigates the effect of the gap ratio of the profiled reed groove (β) on the yarn movement then compares the movements of different yarn kinds. The simulation results indicate that a larger β not only decreases gas leaks (thus saves gas consumption), but also stabilizes the yarn movement. Our simulation results also show that the movement of the yarn of polypropylene is more stable than the other two weft-yarn materials. An experiment is also conducted to validate our numerical results, which shows a favorable agreement between them. Our numerical results of the yarn movement in the profiled reed groove can provide a valuable insight into the optimization of the weft insertion system of the air-jet loom.

scholarly journals Numerical modeling of fluid resonance in narrow gaps of fixed rectangular structures

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401987230
Author(s):  
Ming-ming Liu ◽  
Rui-jia Jin ◽  
Zhen-dong Cui
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Stokes Equations ◽  
Theoretical Data ◽  
Numerical Results ◽  
Two Dimensional ◽  
Arbitrary Lagrangian Eulerian ◽  
Fluid Resonance ◽  
Resonance Wave ◽  
Narrow Gaps

A two-dimensional numerical model is developed to investigate the phenomenon of resonance in narrow gaps. Instead of using commonly used Volume of Fluid method to capture the free surface which is sometimes difficult to capture the geometric properties of the geometrically complicated interface, the free surface is traced by using Arbitrary Lagrangian–Eulerian method. The numerical model is based on the two-dimensional Reynolds-Averaged Navier–Stokes equations. The numerical model is validated against wave propagation in wave flume. Comparisons between the numerical results and available theoretical data show satisfactory agreements. Fluid resonance in narrow gaps of fixed rectangular structures are simulated. Numerical results show that resonance wave height and wave frequency for rectangle boxes with sphenoid corners is larger than for rectangle boxes.

Parallel numerical simulation with domain decomposition for the fluid-filled drum crash

2008 ◽  
Vol 222 (3) ◽  
pp. 319-328 ◽  
Author(s):  
Z Li ◽  
X-L Jin ◽  
X-D Chen
Keyword(s):  
Domain Decomposition ◽  
Structural Dynamics ◽  
Dynamic Behaviour ◽  
Three Dimensional ◽  
Structural Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Structure Interaction ◽  
Ale Finite Element Method ◽  
Control Mesh ◽  
Critical Aspects

Fluid—structure interaction (FSI) problems simultaneously bring together some of the critical aspects associated with both fluid dynamics and structural dynamics. In this research, the simulation of the three-dimensional flexible fluid-filled drum in the crash is achieved through multi-material arbitrary Lagrangian-Eulerian (ALE) finite-element method because of its ability to control mesh geometry independently from geometry. The ALE description is adopted for the fluid domain, whereas for the structural domain the Lagrangian formulation is adopted. The computation of the FSI and the crash contact between the drum and the ground is realized by the penalty-based coupling method. Then the dynamic behaviour of the drum in the crash is analysed and the parallelism is discussed because the computation of the FSI and the crash contact is quite time-consuming. Based on domain decomposition, the recursive coordinate bisection (RCB) is improved according to the time-consuming characteristics of the fluid-filled container in the crash. The results indicate, in comparison with RCB method, the improved recursive coordinate bisection method has improved the speedup and the parallel efficiency.

Extrapolating for attaining high precision solutions for fractional partial differential equations

2018 ◽  
Vol 21 (6) ◽  
pp. 1506-1523 ◽  
Author(s):  
Fernanda Simões Patrício ◽  
Miguel Patrício ◽  
Higinio Ramos
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Precision ◽  
Euler Method ◽  
Accurate Solution ◽  
Numerical Results ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Temporal Integrator ◽  
Present Technique

Abstract This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.

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