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We report measurements of the mean settling velocities for suspensions of discs and rods in the stokes regime for a number of particle aspect ratios. All these shapes display ''hindered settling'', namely, a decrease in settling speed as…

Soft Condensed Matter · Physics 2025-04-24 Yating Zhang , Narayanan Menon

An improved understanding of the divergence-free constraint for the incompressible Navier--Stokes equations leads to the observation that a semi-norm and corresponding equivalence classes of forces are fundamental for their nonlinear…

Numerical Analysis · Mathematics 2019-04-18 Nicolas R. Gauger , Alexander Linke , Philipp W. Schroeder

In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures. Based on the discrete…

Numerical Analysis · Mathematics 2018-10-09 Lorenzo Botti , Daniele A. Di Pietro , Jérôme Droniou

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…

Analysis of PDEs · Mathematics 2023-12-05 Minh-Phuong Tran , Thanh-Nhan Nguyen , Hong-Nhung Nguyen

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…

Applied Physics · Physics 2019-10-22 Elias Karabelas , Gundolf Haase , Gernot Plank , Christoph M. Augustin

We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…

Numerical Analysis · Mathematics 2021-09-14 Jeremias Arf , Bernd Simeon

In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the…

Numerical Analysis · Mathematics 2020-11-04 Lin Mu , Xiu Ye , Shangyou Zhang

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement with the Stark conjecture for imaginary dihedral modular forms of weight $1$. This paper explicitly describes the constants appearing in the…

Number Theory · Mathematics 2024-06-05 Robin Zhang

In this paper we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the…

Numerical Analysis · Mathematics 2023-03-23 Bosco García-Archilla , Julia Novo

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…

Fluid Dynamics · Physics 2016-04-12 Mamdouh S. Mohamed , Anil N. Hirani , Ravi Samtaney

In this study, the nonconforming finite elements of order two and order three are constructed and exploited for the Stokes problem. The moments of order up to $k-1$ ($k=2,3$) on all the facets of the tetrahedron are used for DoFs (degrees…

Numerical Analysis · Mathematics 2022-12-23 Wei Chen , Jun Hu , Min Zhang

We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations…

Quantum Gases · Physics 2015-10-09 J. B. Sudharsan , R. Radha , H. Fabrelli , A. Gammal , Boris A. Malomed

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The element is similar to [C. Taylor and P. Hood, Comput. &…

Numerical Analysis · Mathematics 2023-03-30 Yulei Liao , Pingbing Ming , Yun Xu

Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…

Numerical Analysis · Mathematics 2015-07-28 Gustavo C. Buscaglia

In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the…

Analysis of PDEs · Mathematics 2024-04-02 Jaemin Park

A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus…

Fluid Dynamics · Physics 2021-02-24 Pankaj Jagad , Abdullah Abukhwejah , Mamdouh Mohamed , Ravi Samtaney

We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. In the sequel to Ammari, Waters, Zhang (2015), we use pseudodifferential methods for the problem of…

Analysis of PDEs · Mathematics 2015-10-19 Heiko Gimperlein , Alden Waters

We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with $(r,\epsilon)$-structure. Thereby the velocity-errors are independent of the pressure-error; i.e., the method is…

Numerical Analysis · Mathematics 2025-01-28 Lars Diening , Adrian Hirn , Christian Kreuzer , Pietro Zanotti