Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Bellotti, Thomas"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G7, Pp 761-769 (2022)
We consider an adaptive multiresolution-based lattice Boltzmann scheme, which we have recently introduced and studied from the perspective of the error control and the theory of the equivalent equations. This numerical strategy leads to high compress
Externí odkaz:
https://doaj.org/article/b6f68e3be0c14fac9cdcfc09a8a8a290
Autor:
Bellotti, Thomas
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme. By mapping lattice Boltzmann schemes to Finite Difference schemes, we facilitate rigorous consistency and stability analyses. We deve
Externí odkaz:
http://arxiv.org/abs/2407.02009
We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical schemes for hyperbolic problems, high-order accuracy applies only to
Externí odkaz:
http://arxiv.org/abs/2403.13406
Autor:
Bellotti, Thomas
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of multiple roots
Externí odkaz:
http://arxiv.org/abs/2312.14503
Autor:
Bellotti, Thomas
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical s
Externí odkaz:
http://arxiv.org/abs/2302.07558
Autor:
Bellotti, Thomas
Publikováno v:
ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57, pp.1225-1255
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency analysis and t
Externí odkaz:
http://arxiv.org/abs/2205.02505
Autor:
Bellotti, Thomas
Publikováno v:
In Computers and Mathematics with Applications 15 November 2024 174:397-416
Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the well-know
Externí odkaz:
http://arxiv.org/abs/2201.05354
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to construct
Externí odkaz:
http://arxiv.org/abs/2105.13816