A NURBS-based discontinuous Galerkin method for conservation laws with high-order moving meshes
نویسندگان
چکیده
The objective of the present work is to develop a new numerical framework for simulations involving deformable domains, in specific context high-order meshes consistent with Computer-Aided Design (CAD) representations. Thus, proposed approach combines ideas from isogeometric analysis, able handle exactly CAD-based geometries, and Discontinuous Galerkin (DG) methods an Arbitrary Lagrangian-Eulerian (ALE) formulation, solve complex problems moving grids. resulting DG method based on rational Bézier elements, that can be easily constructed Non-Uniform Rational B-Splines (NURBS), formulated general ALE setting. We focus here applications two-dimensional compressible flows, but could applied other models as well. Two verification exercises are conducted, assess rigorously properties convergence rates representations up sixth order. Finally, three analysed depth, Euler Navier-Stokes equations, oscillating cylinder pitching airfoil. In particular, flow characteristics investigated, well impact using curved boundaries domains.
منابع مشابه
Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws
In this paper, a moving mesh discontinuous Galerkin (DG) method is developed to solve the nonlinear conservation laws. In the mesh adaptation part, two issues have received much attention. One is about the construction of the monitor function which is used to guide the mesh redistribution. In this study, a heuristic posteriori error estimator is used in constructing the monitor function. The se...
متن کاملA sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes
We present a new line-based discontinuous Galerkin (DG) discretization scheme for firstand second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the collocation-based DG spectral element method (DGSEM) or...
متن کاملThe Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the...
متن کاملThe Discontinuous Galerkin Method for Fractal Conservation Laws
We propose, analyze, and demonstrate a discontinuous Galerkin method for fractional conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and when piecewise constant elements are utilized, we prove a rate of convergence toward the unique entropy solution. We present numerical results f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2021
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2020.110093