scholarly journals An Adaptive Mesh Algorithm: Mapping the Mesh Variables

2016 ◽  
Author(s):  
Anthony J. Scannapieco
Keyword(s):  
Adaptive Mesh ◽  
Algorithm Mapping

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

Dynamic structural analysis of connecting rod through adaptive mesh refinement for different materials

2018 ◽  
Vol 50 (04) ◽  
pp. 561-570
Author(s):  
I. A. QAZI ◽  
A. F. ABBASI ◽  
M. S. JAMALI ◽  
INTIZAR INTIZAR ◽  
A. TUNIO ◽  
...  
Keyword(s):  
Structural Analysis ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Connecting Rod ◽  
Dynamic Structural Analysis

scholarly journals Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains

Atmosphere ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 444 ◽  
Author(s):  
Jinxi Li ◽  
Jie Zheng ◽  
Jiang Zhu ◽  
Fangxin Fang ◽  
Christopher. Pain ◽  
...  
Keyword(s):  
Unstructured Mesh ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Galerkin Finite Element Method ◽  
Adaptive Meshes ◽  
Galerkin Finite Element ◽  
Computational Costs ◽  
Cut Cell ◽  
Discontinuous Galerkin Finite Element ◽  
Terrain Following

Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs.

scholarly journals Insights into the physics when modelling cold gas clouds in a hot plasma

2019 ◽  
Vol 490 (1) ◽  
pp. L52-L56
Author(s):  
Bastian Sander ◽  
Gerhard Hensler
Keyword(s):  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Careful Consideration ◽  
Necessary Condition ◽  
Interstellar Clouds ◽  
Hot Plasma ◽  
Magnetic Dipole Field ◽  
Set Up ◽  
Self Gravity ◽  
Cold Gas

ABSTRACT This paper aims at studying the reliability of a few frequently raised, but not proven, arguments for the modelling of cold gas clouds embedded in or moving through a hot plasma and at sensitizing modellers to a more careful consideration of unavoidable acting physical processes and their relevance. At first, by numerical simulations we demonstrate the growing effect of self-gravity on interstellar clouds and, by this, moreover argue against their initial set-up as homogeneous. We apply the adaptive-mesh refinement code flash with extensions to metal-dependent radiative cooling and external heating of the gas, self-gravity, mass diffusion, and semi-analytic dissociation of molecules, and ionization of atoms. We show that the criterion of Jeans mass or Bonnor–Ebert mass, respectively, provides only a sufficient but not a necessary condition for self-gravity to be effective, because even low-mass clouds are affected on reasonable dynamical time-scales. The second part of this paper is dedicated to analytically study the reduction of heat conduction by a magnetic dipole field. We demonstrate that in this configuration, the effective heat flow, i.e. integrated over the cloud surface, is suppressed by only 32 per cent by magnetic fields in energy equipartition and still insignificantly for even higher field strengths.

scholarly journals Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

2021 ◽  
Author(s):  
Alexander Haberl ◽  
Dirk Praetorius ◽  
Stefan Schimanko ◽  
Martin Vohralík
Keyword(s):  
Adaptive Algorithm ◽  
Adaptive Mesh Refinement ◽  
Elliptic Boundary ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Picard Iteration ◽  
Optimal Rate ◽  
Stopping Criteria ◽  
Element Discretization ◽  
Fully Adaptive

AbstractWe consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach–Picard linearization, and a contractive linear algebraic solver. In particular, we identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach–Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach–Picard iteration that leave an amount of linearization error that is not harmful for the residual a posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement/linearization/algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.

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