Adaptive zoning for singular problems in two dimensions

Brackbill, J. U.; Saltzman, J.

doi:10.1016/0021-9991(82)90020-1

Cited by 530 publications

(319 citation statements)

References 9 publications

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“…It seems plausible to include these additional properties, starting again by a variational principle in the computational domain with the corresponding extra terms as in [10,11]. In general, the monitor function in the mesh generator should be problem-dependent as this function ultimately determines the compression and deformation of the mesh.…”

Section: Discussionmentioning

confidence: 99%

“…Here p denotes the physical domain. More terms can be added to the functional (1) to control other aspects of the mesh such as orthogonality (skewness) and mesh alignment with a given vector field [10,11]. There are also adaptive meshes based directly on a discrete variational principle [15,16].…”

Section: Classical Variational Mesh Generationmentioning

confidence: 99%

“…Then, beginning with an initial guess, we march in "time" to steady state. Any discrete marching scheme to solve (11) and (12) can be regarded as an iterative method to solve the nonlinear system (9). At t = 0, we can find the solution to (11)- (12) up to steady state to obtain a mesh that adapts well to the initial data.…”

Section: The Moving Meshmentioning

confidence: 99%

“…Then a new mesh is obtained using the updated u in the monitor function. However, since u changes only very little in one time step, it is not necessary to solve again (11) and (12) all the way to steady state. Besides, the initial mesh is already a very good initial guess.…”

Section: The Moving Meshmentioning

confidence: 99%

See 3 more Smart Citations

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

Ceniceros¹,

Hou²

2001

Journal of Computational Physics

148

156

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We develop an efficient dynamically adaptive mesh generator for time-dependent problems in two or more dimensions. The mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic PDEs for the mesh map. When coupled to a physical problem, the mesh map evolves with the underlying solution and maintains high adaptivity as the solution develops complicated structures and even singular behavior. The overall mesh strategy is simple to implement, avoids interpolation, and can be easily incorporated into a broad range of applications. The efficacy of the mesh is first demonstrated by two examples of blowing-up solutions to the 2-D semilinear heat equation. These examples show that the mesh can follow with high adaptivity a finite-time singularity process. The focus of applications presented here is however the baroclinic generation of vorticity in a strongly layered 2-D Boussinesq fluid, a challenging problem. The moving mesh follows effectively the flow resolving both its global features and the almost singular shear layers developed dynamically. The numerical results show the fast collapse to small scales and an exponential vorticity growth.

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Section: Discussionmentioning

confidence: 99%

Section: Classical Variational Mesh Generationmentioning

confidence: 99%

Section: The Moving Meshmentioning

confidence: 99%

Section: The Moving Meshmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

Ceniceros¹,

Hou²

2001

Journal of Computational Physics

148

156

View full text Add to dashboard Cite

show abstract

“…The original technique was developed by Brackbill and Saltzman [9] who used the variational method to minimizing a linear combination of integrals which are measures of different grid characteristics, including smoothness, orthogonality and weighted cell area of the grids. To add the multizoning feature, this technique was modified by using constrained variational minimization on the grid line that separates two zones, thus, permitting the grid nods to move along this interface line only.…”

Section: Methodsmentioning

confidence: 99%

Multizone Adaptive Grid Generation Technique for Multilayer Multistep Process Simulation

Moallemi¹,

Zhang²

1993

Simulation of Semiconductor Devices and Processes

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Adaptive mesh-updating methods for non-linear finite element analysis of shells

Nordlund

Giannakopoulos²,

Häggblad

1998

Int. J. Numer. Meth. Engng.

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We consider methods for adaptive updating of computational meshes during incremental loading of non-linear shell and solid structures. In particular, we focus on updating methods where the initial topology of the mesh is maintained. The movement of the mesh (the convective step) is decoupled from the Lagrangian solution step and is done by using separately computed displacement fields, obtained by solving auxiliary thermoelastic problems. The properties of this mesh-updating procedure are investigated and demonstrated on several examples.

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Adaptive zoning for singular problems in two dimensions

Cited by 530 publications

References 9 publications

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

Multizone Adaptive Grid Generation Technique for Multilayer Multistep Process Simulation

Adaptive mesh-updating methods for non-linear finite element analysis of shells

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