BoSSS: A package for multigrid extended discontinuous Galerkin methods

Numerical Methods in Fluids

2021

Self Cite

In this work, an extended discontinuous Galerkin (extended DG/XDG also called unfitted DG) solver for two‐dimensional flow problems exhibiting moving contact lines is presented. The generalized Navier boundary condition is employed within the XDG discretization for the handling of the moving contact lines. The spatial discretization is based on a symmetric interior penalty method and the numerical treatment of the surface tension force is done via the Laplace–Beltrami formulation. The XDG method adapts the approximation space conformal to the position of the interface and allows a sub‐cell accurate representation within the sharp interface formulation. The interface is described as the zero set of a signed‐distance level‐set function and discretized by a standard DG method. No adaption of the level‐set evolution algorithm is needed for the extension to moving contact line problems. The developed solver is validated against typical two‐dimensional contact line driven flow phenomena including droplet simulations on a wall and the two‐phase Couette flow.

Section: Numerical Resultsmentioning

confidence: 99%

The extended discontinuous Galerkin method adapted for moving contact line problems via the generalized Navier boundary condition

Smuda

Numerical Methods in Fluids

2021

Self Cite

“…A corresponding basis to the agglomerated mesh Agg(𝔎 X h (t)) is denoted by 𝚽 X,𝛼 (t). For details on the mesh agglomeration algebra, we refer to the work of Kummer et al 31 Regarding the implementation of this procedure, see Section 6.…”

Section: Cell Agglomerationmentioning

confidence: 99%

“…which is introduced within the moving interface approach. 11 The discretized problem (31) needs to be solved iteratively due to the nonlinearity of the convective term. Thus, the whole system is linearized in each iteration with u * .…”

Section: Xdg Discretization Of the Incompressible Two-phase Nse In Xdgmentioning

confidence: 99%

“…Finally, we specify the term s(v, q) on the right-hand side of the variational formulation (31), which summarizes the Dirichlet boundary conditions and force terms…”

Section: Xdg Discretization Of the Incompressible Two-phase Nse In Xdgmentioning

confidence: 99%

“…In this section the coupling of the flow solver for the discretized system (31) and the interface evolution is presented. Additionally, the adaptive mesh refinement (AMR) procedure is briefly discussed at the end.…”

Section: Solver Structure-coupling Flow Solver and Interface Evolutionmentioning

confidence: 99%

See 2 more Smart Citations

On a marching level‐set method for extended discontinuous Galerkin methods for incompressible two‐phase flows: Application to two‐dimensional settings

Smuda

Numerical Meth Engineering

2021

Self Cite

In this work a solver for two-dimensional, instationary two-phase flows on the basis of the extended discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This allows a subcell accurate representation of the incompressible Navier-Stokes equations in their sharp interface formulation. The interface is described as the zero set of a signed-distance level-set function and discretized by a standard DG method. For the interface, resp. level-set, evolution an extension velocity field is used and a two-staged algorithm is presented for its construction on a narrow-band. On the cut-cells a monolithic elliptic extension velocity method is adapted and a fast-marching procedure on the neighboring cells. The spatial discretization is based on a symmetric interior penalty method and for the temporal discretization a moving interface approach is adapted. A cell agglomeration technique is utilized for handling small cut-cells and topology changes during the interface motion. The method is validated against a wide range of typical two-phase surface tension driven flow phenomena in a 2D setting including capillary waves, an oscillating droplet and the rising bubble benchmark.

A fully coupled high‐order discontinuous Galerkin method for diffusion flames in a low‐Mach number framework

Gutiérrez-Jorquera

Numerical Methods in Fluids

2021

Self Cite

We present a fully coupled solver based on the discontinuous Galerkin method for steady‐state diffusion flames using the low‐Mach approximation of the governing equations with a one‐step kinetic model. The nonlinear equation system is solved with a Newton–Dogleg method and initial estimates for flame calculations are obtained from a flame‐sheet model. Details on the spatial discretization and the nonlinear solver are presented. The method is tested with reactive and nonreactive benchmark cases. Convergence studies are presented, and we show that the expected convergence rates are obtained. The solver for the low‐Mach equations is used for calculating a differentially heated cavity configuration, which is validated against benchmark solutions. Additionally, a two‐dimensional counter diffusion flame is calculated, and the results are compared with the self‐similar one dimensional solution of said configuration.