On the shape of tetrahedra from bisection
Mathematics of Computation
Curvature flow and entropy conditions applied to grid generation
Journal of Computational Physics
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
A projection method for locally refined grids
Journal of Computational Physics
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
Journal of Computational Physics
Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
SIAM Journal on Scientific Computing
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
A method for capturing sharp fluid interfaces on arbitrary meshes
Journal of Computational Physics
An adaptive version of the immersed boundary method
Journal of Computational Physics
Level-set-based deformation methods for adaptive grids
Journal of Computational Physics
An iterative grid redistribution method for singular problems in multiple dimensions
Journal of Computational Physics
Journal of Computational Physics
The geometric integration of scale-invariant ordinary and partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Locally Adapted Tetrahedral Meshes Using Bisection
SIAM Journal on Scientific Computing
A P1 - P1 Finite Element Method for a Phase Relaxation Model II: Adaptively Refined Meshes
SIAM Journal on Numerical Analysis
An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
SIAM Journal on Numerical Analysis
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
An auxiliary grid method for computations of multiphase flows in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
Tracking discontinuities in hyperbolic conservation laws with spectral accuracy
Journal of Computational Physics
Transient adaptivity applied to two-phase incompressible flows
Journal of Computational Physics
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Local remeshing for large amplitude grid deformations
Journal of Computational Physics
Algorithm for direct numerical simulation of emulsion flow through a granular material
Journal of Computational Physics
Journal of Computational Physics
Implicit tracking for multi-fluid simulations
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.50 |
We present an adaptive remeshing algorithm for meshes of unstructured triangles in two dimensions and unstructured tetrahedra in three dimensions. The algorithm automatically adjusts the size of the elements with time and position in the computational domain in order to resolve the relevant scales in multiscale physical systems to a user-prescribed accuracy while minimizing computational cost. The optimal mesh that provides the desired resolution is achieved by minimizing a spring-like mesh energy function that depends on the local physical scales using local mesh restructuring operations that include edge-swapping, element insertion/removal, and dynamic mesh-node displacement (equilibration). The algorithm is a generalization to volume domains of the adaptive surface remeshing algorithm developed by Cristini et al. [V. Cristini, J. Blawzdziewicz, M. Loewenberg, An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comp. Phys., 168 (2001) 445] in the context of deforming interfaces in two and three dimensions. The remeshing algorithm is versatile and can be applied to a number of physical and biological problems, where the local length scales are dictated by the specific problem. In Part II [X. Zheng, J. Lowengrub, A. Anderson, V. Cristini, Adaptive unstructured volume remeshing - II: application to two- and three-dimensional level-set simulations of multiphase flow, J. Comp. Phys., in press], we illustrate the performance of an implementation of the algorithm in finite-element/level-set simulations of deformable droplet and fluid-fluid interface interactions, breakup and coalescence in multiphase flows.