Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization

Ju, Lili; Wu, Wensong; Zhao, Weidong

doi:10.3934/dcdsb.2009.11.669

Cited by 6 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, it is essential to properly construct the transition mesh. Due to the above issues, we use the ACVT algorithm [11,27,28,9] as a mesh generator because of its optimality and robustness. The following algorithms and theorems are taken from [11].…”

Section: Anisotropic Centroidal Voronoi Tessellations (Acvt)mentioning

confidence: 99%

Adaptive anisotropic meshing for steady convection-dominated problems

Nguyen

Gunzburger

et al. 2009

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

Obtaining accurate solutions for convection-diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov-Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.

show abstract

Section: Anisotropic Centroidal Voronoi Tessellations (Acvt)mentioning

confidence: 99%

Adaptive anisotropic meshing for steady convection-dominated problems

Nguyen

Gunzburger

et al. 2009

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to overcome this difficulty upwind finite volume methods (UFVM) were proposed for solution of convection-dominated problems and had been quite successful in flow and heat simulations [11,24,28,7,4,13]. Although being numerically stable for solving this type of problems, the standard upwind approximations suffer from bad accuracy mostly due to their first-order local truncation errors.…”

Section: Introductionmentioning

confidence: 99%

Covolume-upwind finite volume approximations for linear elliptic partial differential equations

Xiao

et al. 2012

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

“…Recently, attention has also been paid to vertexcentered finite volume methods. Let us mention, in the steady convection-diffusion-reaction case and energy norm setting, Lazarov and Tomov [17], Carstensen et al [7], Nicaise [18], [30], and Ju et al [16]. Fewer results are known in the unsteady case.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error estimates for combined finite volume–finite element discretizations of reactive transport equations on nonmatching grids

Hilhorst¹,

Vohralı́k²

2011

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

We derive fully computable a posteriori error estimates for vertex-centered finite volume-type discretizations of transient convection-diffusion-reaction equations. Our estimates enable actual control of the error measured either in the energy norm or in the energy norm augmented by a dual norm of the skew-symmetric part of the differential operator. Lower bounds, global-in-space but local-in-time, are also derived. These lower bounds are fully robust with respect to convection or reaction dominance and the final simulation time in the augmented norm setting. On the basis of the derived estimates, we propose an adaptive algorithm which enables to automatically achieve a user-given relative precision. Moreover, this algorithm leads to optimal efficiency as it balances the time and space error contributions. As an example, we apply our estimates to the combined finite volume-finite element scheme, including such features as use of mass lumping for the time evolution or reaction terms, of upwind weighting for the convection term, and discretization on nonmatching meshes possibly containing nonconvex and non-star-shaped elements. Numerical experiments illustrate the theoretical developments.

show abstract

Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization

Cited by 6 publications

References 0 publications

Adaptive anisotropic meshing for steady convection-dominated problems

Adaptive anisotropic meshing for steady convection-dominated problems

Covolume-upwind finite volume approximations for linear elliptic partial differential equations

A posteriori error estimates for combined finite volume–finite element discretizations of reactive transport equations on nonmatching grids

Contact Info

Product

Resources

About