Adaptive Multiscale Methods for Flow Problems: Recent Developments

Dahmen, Wolfgang; Hovhannisyan, Nune; Müller, Siegfried

doi:10.1007/978-3-642-04088-7_4

Cited by 2 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Multiwavelets (MW) are directly compatible with the piecewise-polynomial bases of FV and DG solvers and provide a multiresolution analysis that enables a dynamically adaptive solution that overcomes known shortcomings of conventional adaptive mesh refinement methods (Dahmen, 1997;Cohen et al, 2001;Müller, 2003;Lamby et al, 2005;Díaz Calle et al, 2005;Smith et al, 2008;Dahmen et al, 2010;Archibald et al, 2011;Hovhannisyan et al, 2013;Haleem et al, 2015;Kesserwani et al, 2015;Gerhard et al, 2015b;Gerhard and Müller, 2016;Guo and Cheng, 2016;Wang et al, 2016;Sharifian et al, 2019;Tao et al, 2019). Kesserwani et al (2019) adopted multiwavelets and Haar wavelets to formulate adaptive one-dimensional (1D) MWDG2 and HFV1 hydrodynamic solvers, and found that the 1D-MWDG2 solver achieved the accuracy of the uniform DG2 solver for a runtime cost less than the uniform FV1 solver.…”

Section: Introductionmentioning

confidence: 99%

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches

Kesserwani

Sharifian

2020

Advances in Water Resources

View full text Add to dashboard Cite

Multiwavelets (MW) enable the compression, analysis and assembly of model data on a multiresolution grid withinGodunov-type solvers based on second-order discontinuous Galerkin (DG2) and first-order finite volume (FV1) methods.Multiwavelet adaptivity has been studied extensively with one-dimensional (1D) hydrodynamic models (Kesserwani et al., 2019), revealing that MWDG2 can be 20 times faster than uniform DG2 and 2 times faster than uniform FV1, while preserving the accuracy and robustness of the underlying formulation. The potential of the MWDG2 scheme has yet to be studied for two-dimensional (2D) modelling, but this requires a design that robustly and efficiently solves the 2D shallow water equations (SWE) with complex source terms and wetting and drying. This paper presents a two-dimensional MWDG2 scheme that: (1) adopts a slope-decoupled DG2 solver as a reference scheme, for its ability to deliver well-balanced piecewise-planar solutions shaped by a simplified 3-component basis; and, (2) adapts the multiresolution analysis of multiwavelets for compatibility with the slope-decoupled DG2 basis. A scaled reformulation of slope-decoupled DG2 is presented alongside two multiwavelet approaches that yield MWDG2 schemes with similar properties, and a Haar wavelet FV1 (HFV1) variant for adapting piecewise-constant model data. The performance of the adaptive HFV1 and MWDG2 solvers is explored alongside their uniform counterparts, while analysing their accuracy, efficiency, grid-coarsening ability, reliability in handling wet-dry fronts across steep bed-slopes, and ability to capture features relevant to practical hydraulic modelling. The results indicate a particular multiwavelet approach that allows the MWDG2 scheme to exploit its grid-coarsening ability for the widest range of flow types. Results also indicate that the proposed (multi)wavelet-based adaptive schemes are even more efficient for the 2D case. Accompanying model software is openly available online.

show abstract

Section: Introductionmentioning

confidence: 99%

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches

Kesserwani

Sharifian

2020

Advances in Water Resources

View full text Add to dashboard Cite

show abstract

“…These provide advantages for various application cases, as detailed in a recent survey [BLP*13], where they are deemed ‘the most important class [of quad meshes] in terms of applications’. For instance, they enable the application of efficient adaptive and multi‐level solver schemes [BDL10, DHM09] in the context of quad‐based finite element simulation and the application of degree adaptation techniques in the context of isogeometric analysis [HCB05, Bom12]. Their high level of structuredness is of benefit for applications like mesh compression [AG05] and Fourier or wavelet‐based processing [AUGA08].…”

Section: Introductionmentioning

confidence: 99%

Partitioning Surfaces Into Quadrilateral Patches: A Survey

Campen

2017

Computer Graphics Forum

View full text Add to dashboard Cite

The efficient and practical representation and processing of geometrically or topologically complex shapes often demands a partitioning into simpler patches. Possibilities range from unstructured arrangements of arbitrarily shaped patches on the one end, to highly structured conforming networks of all‐quadrilateral patches on the other end of the spectrum. Due to its regularity, this latter extreme of conforming partitions with quadrilateral patches, called quad layouts, is most beneficial in many application scenarios, for instance enabling the use of tensor‐product representations based on splines or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based map representations. However, this type of partition is also most complicated to create due to the strict inherent structural restrictions. Traditionally often performed manually in a tedious and demanding process, research in computer graphics and geometry processing has led to a number of computer‐assisted, semi‐automatic, as well as fully automatic approaches to address this problem more efficiently. This survey provides a detailed discussion of this range of methods, treats their strengths and weaknesses and outlines open problems in this field of research.

show abstract

Adaptive Multiscale Methods for Flow Problems: Recent Developments

Cited by 2 publications

References 27 publications

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches

Partitioning Surfaces Into Quadrilateral Patches: A Survey

Contact Info

Product

Resources

About