Moving Mesh Methods Based on Moving Mesh Partial Differential Equations

Huang, Weizhang; Ren, Yuhe; Russell, Robert D.

doi:10.1006/jcph.1994.1135

Cited by 198 publications

(189 citation statements)

References 13 publications

Supporting

Mentioning

187

Contrasting

Order By: Relevance

“…[1,3,22,33,37,39,40]). Here, we adopt the so-called moving mesh PDE approach [31][32][33] in which a time-dependent PDE is introduced to determine the motion of the mesh. Both the moving mesh PDE (MMPDE) and the underlying physical equations are solved simultaneously or alternately.…”

Section: The Moving Meshmentioning

confidence: 99%

“…In the computational variables ξ and η, the stream function equation (31) becomes an elliptic equation with variable coefficients. This equation is subjected to Dirichlet boundary conditions (ψ = 0) on the top and bottom of the computational domain and periodic boundary conditions in the horizontal direction.…”

Section: Implementation Details For Boussinesq Flow In a Channelmentioning

confidence: 99%

See 1 more Smart Citation

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

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.

show abstract

Section: The Moving Meshmentioning

confidence: 99%

Section: Implementation Details For Boussinesq Flow In a Channelmentioning

confidence: 99%

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 second step is to generate the adaptive mesh in physical space by defining a unique one-dimensional map from computational space ζ ∈ [0, 1] to physical space which connects intervals of a prescribed length. Finally, the variables in control space generated at points ζ are then interpolated to the levels z (Huang et al, 1994;Tang, 2005;Budd et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

A new implementation of the adaptive mesh transform in the Met Office 3D‐Var System

Piccolo

Cullen

2012

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

“…We use the same problem parameters as in [1] namely, a = 1 and R = 5. We use δ = 30 as in [26,39] since the flame layer in this case is much thinner, and higher mesh adaptation is required. We use (27) to discretize u xx and use a second-order TVD RK scheme [40] for temporal integration.…”

Section: Examplementioning

confidence: 99%

Adaptive multiresolution mesh refinement for the solution of evolution PDEs

Jain

Tsiotras

Zhou

2007

2007 46th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

In this paper we propose a novel multiresolution-based adaptive mesh refinement method for solving Initial-Boundary Value Problems (IBVP) for evolution partial differential equations. The proposed algorithm dynamically adapts the grid to any existing or emerging irregularities in the solution, thus refining the grid only at places where the solution exhibits sharp features. The main advantage of the proposed grid adaptation method is that it results in a grid with a fewer number of nodes when compared to adaptive grids generated by other waveletor multiresolution-based mesh refinement techniques. Several examples show the robustness, stability and savings, in terms of the CPU time, of our algorithm.

show abstract

Moving Mesh Methods Based on Moving Mesh Partial Differential Equations

Cited by 198 publications

References 13 publications

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions

A new implementation of the adaptive mesh transform in the Met Office 3D‐Var System

Adaptive multiresolution mesh refinement for the solution of evolution PDEs

Contact Info

Product

Resources

About