arXiv subjects

Cornelis Vuik

Publications and source records attributed to Cornelis Vuik.

22 records · Page 2Linked to original sources

arXiv2021

Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries

In this work, the projection-based embedded discrete fracture model (pEDFM) for corner-point grid (CPG) geometry is developed for simulation of flow and heat transfer in fractured porous media. Unlike classical embedded discrete fracture approaches, this method allows for using any geologically-relevant model with a complex geometry and generic conductivity contrasts between the rock matrix and the fractures (or faults). The mass and energy conservation equations are coupled using the fully-implicit (FIM) scheme, allowing for stable simulation. Independent corner-point grids are imposed on the rock matrix and all fractures. The connectivities between the non-neighboring grid cells are described such that a consistent discrete representation of the embedded fractures occurs within the corner-point grid geometry. Various numerical tests including geologically-relevant and real-field models are conducted to demonstrate the performance of the developed method. It is shown that pEDFM can accurately capture the physical influence of both highly conductive fractures and flow barriers on the flow and heat transfer fields in complex reservoir geometries. This development casts a promising approach for flow simulations of real-field geo-models, increasing the discretization flexibility and enhancing the computational performance for capturing explicit fractures accurately.

physics.comp-ph↗

arXiv2020

The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases.

math.NA↗

arXiv2019

An IGA Framework for PDE-Based Planar Parameterization on Convex Multipatch Domains

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from no more than a description of the boundary contours of the physical domain. A subclass of the multitude of the available parameterization algorithms are those based on the principles of Elliptic Grid Generation (EGG) which, in their most basic form, attempt to approximate a mapping operator whose inverse is composed of harmonic functions. The main challenge lies in finding a formulation of the problem that is suitable for a computational approach and a common strategy is to approximate the mapping operator by means of solving a PDE-problem. PDE-based EGG is well-established in classical meshing and first generalization attempts to spline-based descriptions (as is mandatory in IgA) have been made. Unfortunately, all of the practically viable PDE-based approaches impose certain requirements on the employed spline-basis, in particular global $C^{\geq 1}$-continuity. This paper discusses a PDE-based EGG-algorithm for the generation of planar parameterizations with arbitrary continuity properties (where arbitrary stands for spline bases with global $C^{\geq 0}$-continuity). A major use case of the proposed algorithm is that of multi-patch parameterization, made possible by the support of $C^{\geq 0}$-continuities. This paper proposes a specially-taylored solution algorithm that exploits many characteristics of the PDE-problem and is suitable for large-scale applications. It is discussed for the single-patch case before generalizing its concepts to multipatch settings. This paper is concluded with three numerical experiments and a discussion of the results.

math.NA↗

arXiv2017

On the impact of quantum computing technology on future developments in high-performance scientific computing

Quantum computing technologies have become a hot topic in academia and industry receiving much attention and financial support from all sides. Building a quantum computer that can be used practically is in itself an outstanding challenge that has become the 'new race to the moon'. Next to researchers and vendors of future computing technologies, national authorities are showing strong interest in maturing this technology due to its known potential to break many of today's encryption techniques, which would have significant impact on our society. It is however quite likely that quantum computing has beneficial impact on many computational disciplines. In this article we describe our vision of future developments in scientific computing that would be enabled by the advent of software-programmable quantum computers. We thereby assume that quantum computers will form part of a hybrid accelerated computing platform like GPUs and co-processor cards do today. In particular, we address the potential of quantum algorithms to bring major breakthroughs in applied mathematics and its applications. Finally, we give several examples that demonstrate the possible impact of quantum-accelerated scientific computing on society.

cs.CE↗