scholarly journals A Hybrid High-Order method for creeping flows of non-Newtonian fluids

2021 ◽  
Author(s):  
Michele Botti ◽  
Daniel Castanon Quiroz ◽  
Daniele Di Pietro ◽  
André Harnist
Keyword(s):  
Steady Motion ◽  
Incompressible Fluids ◽  
High Order ◽  
Well Posedness ◽  
Discretization Method ◽  
Order Method ◽  
Numerical Examples ◽  
High Order Method ◽  
Creeping Flows ◽  
General Meshes

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray-Lions scalar problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau-Yasuda models. Numerical examples complete the exposition.

scholarly journals A Nonconforming High-Order Method for the Biot Problem on General Meshes

2016 ◽  
Vol 38 (3) ◽  
pp. A1508-A1537 ◽  
Author(s):  
Daniele Boffi ◽  
Michele Botti ◽  
Daniele A. Di Pietro
Keyword(s):  
High Order ◽  
Order Method ◽  
High Order Method ◽  
General Meshes

scholarly journals A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity

2020 ◽  
Vol 20 (2) ◽  
pp. 227-249 ◽  
Author(s):  
Michele Botti ◽  
Daniele A. Di Pietro ◽  
Pierre Sochala
Keyword(s):  
Single Phase ◽  
High Order ◽  
Discretization Method ◽  
Specific Storage ◽  
Deformable Porous Medium ◽  
Galerkin Scheme ◽  
High Order Method ◽  
Discontinuous Galerkin Scheme ◽  
Three Space ◽  
General Meshes

AbstractIn this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients.

scholarly journals A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes

2016 ◽  
Vol 86 (307) ◽  
pp. 2159-2191 ◽  
Author(s):  
Daniele A. Di Pietro ◽  
Jérôme Droniou
Keyword(s):  
Elliptic Equations ◽  
High Order ◽  
Order Method ◽  
High Order Method ◽  
General Meshes

Theoretical Aspects of a Multidomain High-Order Method for CAA

2003 ◽  
Author(s):  
Ronan Guenanff ◽  
Pierre Sagaut ◽  
Eric Manoha ◽  
Marc Terracol ◽  
Roger Lewandowsky
Keyword(s):  
High Order ◽  
Order Method ◽  
High Order Method

Analysis of a filtered high-order method for CAA

2003 ◽  
pp. 1978-1981 ◽  
Author(s):  
R. Guénanff ◽  
P. Sagaut ◽  
E. Manoha ◽  
R. Lewandowski
Keyword(s):  
High Order ◽  
Order Method ◽  
High Order Method
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