Related papers: A nested polyhedra model of turbulence
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
The objective of this article is to address the discretisation of fractured/faulted poromechanical models using 3D polyhedral meshes in order to cope with the geometrical complexity of faulted geological models. A polytopal scheme is…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
The effect of Kolmogorov-size spherical particles on homogeneous and isotropic turbulence is investigated using particle-resolved direct numerical simulations at a Taylor-scale Reynolds number of $150$. Four monodisperse suspensions of…
It is known that we can always 3-triangulate (i.e. divide into tetrahedra) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to sphere with $p$ handles, shortly $p$-toroids, could not be convex. So, it is…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
Numerical schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence, numerical simulations of wave-like systems lacking proper handling of these…
Given five points in a three-dimensional euclidean space, one can consider five tetrahedra, using those points as vertices. We present a pentagon-like formula containing the product of three volumes of those tetrahedra in its l.h.s. and the…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
Fragmentation process in a cylindrical magnetized cloud is studied with the nested grid method. The nested grid scheme use 15 levels of grids with different spatial resolution overlaid subsequently, which enables us to trace the evolution…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…
A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements of the system move in the plane, and the range of the interaction can be varied from a more local form…
Many time-dependent problems in the field of computational fluid dynamics can be solved using space-time methods. However, such methods can encounter issues with computational cost and robustness. In order to address these issues,…
As global ocean general circulation models are run at eddy-permitting resolutions, reproducing accurate growth rates of baroclinic instabilities is a major concern when choosing a discretization of the equations of motion. From this…
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…