Title:
|
A superconvergent HDG method for stokes flow with strongly enforced symmetry of the stress tensor
|
Author:
|
Giacomini, Matteo; Karkoulias, Alexandros; Sevilla, Rubén; Huerta, Antonio
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
Abstract:
|
The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-018-0855-y |
Abstract:
|
This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel formulation relies on the well-known Voigt notation to strongly enforce the symmetry of the stress tensor. The proposed strategy introduces several advantages with respect to the existing HDG formulations. First, it remedies the suboptimal behavior experienced by the classical HDG method for formulations involving the symmetric part of the gradient of the primal variable. The optimal convergence of the mixed variable is retrieved and an element-by-element postprocess procedure leads to a superconvergent velocity field, even for low-order approximations. Second, no additional enrichment of the discrete spaces is required and a gain in computational efficiency follows from reducing the quantity of stored information and the size of the local problems. Eventually, the novel formulation naturally imposes physical tractions on the Neumann boundary. Numerical validation of the optimality of the method and its superconvergent properties is performed in 2D and 3D using meshes of different element types. |
Abstract:
|
Peer Reviewed |
Subject(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica -Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències -Difference equations--Numerical solutions -Fluid dynamics (Mathematics) -Hybridizable discontinuous Galerkin -Stokes flow -Cauchy stress formulation -Voigt notation -Superconvergence -Equacions diferencials--solucions numèriques -Dinàmica de fluids -Classificació AMS::65 Numerical analysis::65L Ordinary differential equations -Classificació AMS::76 Fluid mechanics::76D Incompressible viscous fluids |
Rights:
|
|
Document type:
|
Article - Submitted version Article |
Share:
|
|