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- research-articleDecember 2020
Mesh generation for thin layered domains and its application to parallel multigrid simulation of groundwater flow
Computing and Visualization in Science (COVS), Volume 23, Issue 1-4https://doi.org/10.1007/s00791-020-00322-5AbstractThe generation of detailed three dimensional meshes for the simulation of groundwater flow in thin layered domains is crucial to capture important properties of the underlying domains and to reach a satisfying accuracy. At the same time, this ...
- research-articleJanuary 2020
An RBF-FD sparse scheme to simulate high-dimensional Black–Scholes partial differential equations
Computers & Mathematics with Applications (CMAP), Volume 79, Issue 2Pages 426–439https://doi.org/10.1016/j.camwa.2019.07.011AbstractThe objective of this research is to investigate the numerical solution of high-dimensional Black–Scholes partial differential equations (PDEs). To do this, the weights of the radial basis function-finite difference (RBF-FD) scheme ...
- research-articleJanuary 2020
An efficient algorithm for the calculation of sub-grid distances for higher-order LBM boundary conditions in a GPU simulation environment
Computers & Mathematics with Applications (CMAP), Volume 79, Issue 1Pages 66–87https://doi.org/10.1016/j.camwa.2018.04.022AbstractThis paper presents a new and efficient algorithm for the calculation of sub-grid distances in the context of a lattice Boltzmann method (LBM). LBMs usually operate on equidistant Cartesian grids and represent moving geometries by ...
- research-articleJanuary 2020
Automatic triangular grid generation on a free-form surface using a particle self-organizing system
Engineering with Computers (ENGC), Volume 36, Issue 1Pages 377–389https://doi.org/10.1007/s00366-019-00705-4AbstractA novel method for automatic triangular grid generation on a free-form surface based on Coulomb’s law is proposed in this paper, which we refer to as the particle self-organizing system (PSOS). The self-organizing of particles is realized by the ...
- research-articleSeptember 2019
On the solution of 3D problems in physics: From the geometry definition in CAD to the solution by a meshless method
Journal of Computational Physics (JOCP), Volume 393, Issue CPages 351–374https://doi.org/10.1016/j.jcp.2019.05.007AbstractThis paper presents a simple meshfree approach, from the grid generation to the final solution, for the simulation of 3D problems geometrically defined by CAD. First, the domain grid for 3D problems is generated through a discrete ...
Highlights- Automatic/systematic determination of parameters in the exponential basis functions.
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- research-articleAugust 2019
A triangular grid generation and optimization framework for the design of free-form gridshells
Computer-Aided Design (CADE), Volume 113, Issue CPages 96–113https://doi.org/10.1016/j.cad.2019.04.005AbstractGridshells have been widely used in various public buildings, and many of them are defined over complex free-form surfaces with complex boundaries. This emphasizes the importance of general grid generation and optimization methods in ...
Highlights- Framework presented for automatic triangular grid generation over free-form surfaces with complex boundaries.
- research-articleJuly 2019
Accelerating advancing layer viscous mesh generation for 3D complex configurations
Computer-Aided Design (CADE), Volume 112, Issue CPages 35–46https://doi.org/10.1016/j.cad.2018.11.002AbstractThis paper describes the implementation of an efficient and robust advancing layer viscous mesh generation method for complex 3D configurations. The method employs a pre-processing algorithm to identify cells that can be generated ...
Highlights- Novel approach to generate hybrid grids for aerodynamic is proposed.
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- research-articleNovember 2017
Generating one-column grids with fractal flow dimension
Computers & Geosciences (CGEO), Volume 108, Issue CPages 33–41https://doi.org/10.1016/j.cageo.2016.11.010The grid generation capability built into the numerical simulator TOUGH for multi-phase fluid and heat flow through geologic media can create one-column grids with linear or radial geometry, corresponding to one-dimensional or two-dimensional radial ...
- research-articleAugust 2017
Grid generation on free-form surface using guide line advancing and surface flattening method
Advances in Engineering Software (ADES), Volume 110, Issue CPages 98–109https://doi.org/10.1016/j.advengsoft.2017.04.003A framework is presented to generate grid pattern for rod distribution on free-form surfaces.Surface flattening technique is used in combination with the guide line method to generate grids.Grids created by combining flattening technique with guide line ...
- research-articleJuly 2017
Integrated framework for solving the convection diffusion equation on 2D Quad mesh relying on internal boundaries
Computers & Mathematics with Applications (CMAP), Volume 74, Issue 1Pages 218–228https://doi.org/10.1016/j.camwa.2017.03.001The aim of this research is the design and implementation of an integrated framework to solve numerically the two-dimensional convection diffusion equations on non-rectangular grids formed only by quadrilaterals honoring the internal structures of an ...
- articleJanuary 2014
A grid generator for 3-D explosion simulations using the staircase boundary approach in Cartesian coordinates based on STL models
Advances in Engineering Software (ADES), Volume 67Pages 148–155https://doi.org/10.1016/j.advengsoft.2013.09.007In this paper, an automatic grid generator based on STL models is proposed. The staircase boundary treatment is implemented to handle irregular geometries and the computation domain is discretized using a regular Cartesian grid. Using the grid generator, ...
- research-articleNovember 2013
Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method
In isogeometric analysis, parameterization of computational domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the computational domain to parametric domain, a variational ...
- articleAugust 2012
Preparation of grids for simulations of groundwater flow in fractured porous media
Computing and Visualization in Science (COVS), Volume 15, Issue 4Pages 209–225https://doi.org/10.1007/s00791-013-0210-7This work presents an extension of grid generation techniques for finite-volume discretizations of density-driven flow in fractured porous media, in which fractures are considered as low-dimensional manifolds and are resolved by sides of grid elements. ...
- articleJanuary 2011
Automatic grid control in adaptive BVP solvers
Grid adaptation in two-point boundary value problems is usually based on mapping a uniform auxiliary grid to the desired nonuniform grid. Here we combine this approach with a new control system for constructing a grid density function ( x ). The local ...
- articleAugust 2010
Numerical analysis and implementational aspects of a new multilevel grid deformation method
Applied Numerical Mathematics (APNM), Volume 60, Issue 8Pages 767–781https://doi.org/10.1016/j.apnum.2010.03.017Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; ...
- articleMay 2009
Comparison of different spatial grids for numerical schemes of geophysical fluid dynamics
Journal of Computational and Applied Mathematics (JCAM), Volume 227, Issue 1Pages 161–170https://doi.org/10.1016/j.cam.2008.07.009The generation of computational grids is an important component contributing to the efficiency of numerical schemes of atmosphere/ocean dynamics. In this study the problem of construction of the most uniform grids based on conformal mappings of ...
- articleApril 2009
A grid redistribution method for singular problems
Journal of Computational Physics (JOCP), Volume 228, Issue 7Pages 2354–2365https://doi.org/10.1016/j.jcp.2008.11.035Many physical phenomena develop singular, or nearly singular behavior in localized regions, e.g. boundary layers or blowup solutions. Using uniform grids for such problems becomes computationally prohibitive as the solution approaches singularity. Ren ...
- articleJanuary 2009
Constrained CVT meshes and a comparison of triangular mesh generators
Computational Geometry: Theory and Applications (COGE), Volume 42, Issue 1Pages 1–19https://doi.org/10.1016/j.comgeo.2008.04.002Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. We focus on ...
- articleDecember 2008
Application of B-spline techniques to the modeling of airplane wings and numerical grid generation
Computer Aided Geometric Design (CAGD), Volume 25, Issue 9Pages 738–750https://doi.org/10.1016/j.cagd.2008.07.010In the present paper we give account of an effort that aimed at the unification of the whole geometric preprocessing that preceded the wind tunnel readings with a realistic airplane wing model in a recent research project. This preprocessing includes ...
- articleMarch 2008
Curvilinear space-filling curves for five-axis machining
Computer-Aided Design (CADE), Volume 40, Issue 3Pages 350–367https://doi.org/10.1016/j.cad.2007.11.007The paper presents a new combination of two methods for tool path generation for five-axis machining proposed earlier by the authors. The first method is based on the grid generation technologies whereas the second method exploits the space-filling ...