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A boundary-fitted moving mesh scheme is presented for the simulation of two-phase flow in two-dimensional and axisymmetric geometries. The incompressible Navier-Stokes equations are solved using the finite element method, and the mini element is used to sa ...
The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeometric methods. We investigate the design and implementati ...
We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splin ...
In this work, we focus on the family of shell formulations referred to as "solid shells", where the simulation of shell-type structures is performed by means of a mesh of 3D solid elements, with typically only one element through the thickness. We propose ...
In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation.
This approach follows the interface with an adaptive moving mesh.
The incompressible Navier-Stokes equations are solved, in tw ...
A moving mesh approach is employed to simulate two-phase flow with phase change. The mathematical model is based on the Arbitrary Lagrangian-Eulerian (ALE) description of the axisymmetric Navier-Stokes equations and energy conservation. These equations are ...
We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and continue the study of its numerical properties. We prove that our AIGM is optimal in the sense that delivers optimal convergence rates as soon as the solutio ...
A method for performing H-spline compatible isogeometric analysis (IGA) on a geometric object, the method being performed on a computer device having a memory, the method including the steps of creating an analysis suitable geometry (ASG) using H-splines f ...
In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be unders ...