Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions

Berninger, Heiko; Ohlberger, Mario; Sander, Oliver; Smetana, Kathrin

doi:10.1142/s0218202513500711

Cited by 12 publications

(14 citation statements)

References 33 publications

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“…high optical depth) or stream outward (i.e. low optical depth) from the explosion [24]. Often intermediate regimes will have no accurate technique available.…”

Section: Discussionmentioning

confidence: 99%

DIAPHANE: A portable radiation transport library for astrophysical applications

Reed

Dykes

Cabezón

et al. 2018

Computer Physics Communications

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One of the most computationally demanding aspects of the hydrodynamical modelling of Astrophysical phenomena is the transport of energy by radiation or relativistic particles. Physical processes involving energy transport are ubiquitous and of capital importance in many scenarios ranging from planet formation to cosmic structure evolution, including explosive events like core collapse supernova or gamma-ray bursts. Moreover, the ability to model and hence understand these processes has often been limited by the approximations and incompleteness in the treatment of radiation and relativistic particles. The diaphane project has focused in developing a portable and scalable library that handles the transport of radiation and particles (in particular neutrinos) independently of the underlying hydrodynamic code. In this work, we present the computational framework and the functionalities of the first version of the diaphane library, which has been successfully ported to three different smoothed-particle hydrodynamic codes, gadget2, gasoline and sphynx. We also present validation of different modules solving the equations of radiation and neutrino transport using different numerical schemes.

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“…high optical depth) or stream outward (i.e. low optical depth) from the explosion [24]. Often intermediate regimes will have no accurate technique available.…”

Section: Discussionmentioning

confidence: 99%

DIAPHANE: A portable radiation transport library for astrophysical applications

Reed

Dykes

Cabezón

et al. 2018

Computer Physics Communications

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“…In the time interval [0, T ] we consider the Richards equation (see e.g. [3,4]) for the water saturation s : Ω × [0, T ] → [0, 1] and the water pressure p :…”

Section: Saturated-unsaturated Subsurface Flowmentioning

confidence: 99%

Approximation of skewed interfaces with tensor-based model reduction procedures: Application to the reduced basis hierarchical model reduction approach

Ohlberger

Smetana

2016

Journal of Computational Physics

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In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of partial differential equations in the presence of interfaces or strong gradients in the solution which are skewed with respect to the coordinate axes. The two key ideas are the location of the interface either by solving a lower-dimensional partial differential equation or by using data functions and the subsequent removal of the interface of the solution by choosing the determined interface as the lifting function of the Dirichlet boundary conditions. We demonstrate in numerical experiments for linear elliptic equations and the reduced basis-hierarchical model reduction approach that the proposed procedure locates the interface well and yields a significantly improved convergence behavior even in the case when we only consider an approximation of the interface.2 An ansatz for approximating skewed interfaces with tensor-based model reduction approachesLet Ω ⊂ R 2 denote the computational domain with Lipschitz boundary ∂Ω, Σ D ⊂ ∂Ω the Dirichlet boundary, and Σ N ⊂ ∂Ω the Neumann boundary. We require that Σ D has

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“…There are several possible models for the surface flow, ranging from the (compressible or incompressible) Navier-Stokes/Euler equations (Temam 2001) to source terms at the fluid-porous interface that represent, e.g., the rainfall rate and act as boundary conditions for the subsurface model (Berninger et al 2014). For creeping flows, the advective inertial forces are small in comparison with the viscous forces, and therefore, the nonlinear inertial terms in the incompressible Navier-Stokes equations can be neglected leading to the Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the porous medium model typically includes multiphase Darcy's law (Helmig 1997) that represents flows of several fluids or Richards' equation (1931) that describes movement of only water through saturated/unsaturated porous media. Coupling of subsurface flows described by the Richards equation and overland flows has been studied recently (Dawson 2008;Rybak et al 2015;Kollet and Maxwell 2006;Sulis et al 2010;Sochala et al 2009;Berninger et al 2014;Mosthaf et al 2011).…”

Section: Introductionmentioning

confidence: 99%

A Hyperbolic–Elliptic Model Problem for Coupled Surface–Subsurface Flow

2015

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We consider a model problem for coupled surface-subsurface flow. The model consists of a nonlinear kinematic wave equation for the surface fluid's height and a Brinkman model that governs fluid velocity and pressure for subsurface dynamics. For this coupled hyperbolic-elliptic model we establish the existence of weak solutions. The proof is based on a viscous approximation and the method of compensated compactness by virtue of appropriate energy estimates. To solve the coupled problem numerically, a finite volume method is applied. The numerical scheme is used to illustrate the influence of the Brinkman parameter on the coupled flow pattern for infiltration scenarios.

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Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions

Abstract: Math. Models Methods Appl. Sci. 2014.24:901-936. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 02/18/15. For personal use only. 902 H. Berninger et al.

Cited by 12 publications

References 33 publications

DIAPHANE: A portable radiation transport library for astrophysical applications

DIAPHANE: A portable radiation transport library for astrophysical applications

Approximation of skewed interfaces with tensor-based model reduction procedures: Application to the reduced basis hierarchical model reduction approach

A Hyperbolic–Elliptic Model Problem for Coupled Surface–Subsurface Flow

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