19 research outputs found
Augmented resolution of linear hyperbolic systems under nonconservative form
Hyperbolic systems under nonconservative form arise in numerous applications
modeling physical processes, for example from the relaxation of more general
equations (e.g. with dissipative terms). This paper reviews an existing class
of augmented Roe schemes and discusses their application to linear
nonconservative hyperbolic systems with source terms. We extend existing
augmented methods by redefining them within a common framework which uses a
geometric reinterpretation of source terms. This results in intrinsically
well-balanced numerical discretizations. We discuss two equivalent
formulations: (1) a nonconservative approach and (2) a conservative
reformulation of the problem. The equilibrium properties of the schemes are
examined and the conditions for the preservation of the well-balanced property
are provided. Transient and steady state test cases for linear acoustics and
hyperbolic heat equations are presented. A complete set of benchmark problems
with analytical solution, including transient and steady situations with
discontinuities in the medium properties, are presented and used to assess the
equilibrium properties of the schemes. It is shown that the proposed schemes
satisfy the expected equilibrium and convergence properties
Analytical and numerical insights into wildfire dynamics: Exploring the advection-diffusion-reaction model
Understanding the dynamics of wildfire is crucial for developing management
and intervention strategies. Mathematical and computational models can be used
to improve our understanding of wildfire processes and dynamics. This paper
presents a systematic study of a widely used advection-diffusion-reaction
wildfire model with non-linear coupling. The importance of single mechanisms is
discovered by analysing hierarchical sub-models. Numerical simulations provide
further insight into the dynamics. As a result, the influence of wind and model
parameters such as the bulk density or the heating value on the wildfire
propagation speed and the remaining biomass after the burn are assessed.
Linearisation techniques for a reduced model provide surprisingly good
estimates for the propagation speed in the full model
Understanding the hydrological response of a headwater-dominated catchment by analysis of distributed surface–subsurface interactions
We computationally explore the relationship between surface–subsurface exchange and hydrological response in a headwater-dominated high elevation, mountainous catchment in East River Watershed, Colorado, USA. In order to isolate the effect of surface–subsurface exchange on the hydrological response, we compare three model variations that differ only in soil permeability. Traditional methods of hydrograph analysis that have been developed for headwater catchments may fail to properly characterize catchments, where catchment response is tightly coupled to headwater inflow. Analyzing the spatially distributed hydrological response of such catchments gives additional information on the catchment functioning. Thus, we compute hydrographs, hydrological indices, and spatio-temporal distributions of hydrological variables. The indices and distributions are then linked to the hydrograph at the outlet of the catchment. Our results show that changes in the surface–subsurface exchange fluxes trigger different flow regimes, connectivity dynamics, and runoff generation mechanisms inside the catchment, and hence, affect the distributed hydrological response. Further, changes in surface–subsurface exchange rates lead to a nonlinear change in the degree of connectivity—quantified through the number of disconnected clusters of ponding water—in the catchment. Although the runoff formation in the catchment changes significantly, these changes do not significantly alter the aggregated streamflow hydrograph. This hints at a crucial gap in our ability to infer catchment function from aggregated signatures. We show that while these changes in distributed hydrological response may not always be observable through aggregated hydrological signatures, they can be quantified through the use of indices of connectivity
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Augmented resolution of linear hyperbolic systems under nonconservative form
Hyperbolic systems under nonconservative form arise in numerous applications
modeling physical processes, for example from the relaxation of more general
equations (e.g. with dissipative terms). This paper reviews an existing class
of augmented Roe schemes and discusses their application to linear
nonconservative hyperbolic systems with source terms. We extend existing
augmented methods by redefining them within a common framework which uses a
geometric reinterpretation of source terms. This results in intrinsically
well-balanced numerical discretizations. We discuss two equivalent
formulations: (1) a nonconservative approach and (2) a conservative
reformulation of the problem. The equilibrium properties of the schemes are
examined and the conditions for the preservation of the well-balanced property
are provided. Transient and steady state test cases for linear acoustics and
hyperbolic heat equations are presented. A complete set of benchmark problems
with analytical solution, including transient and steady situations with
discontinuities in the medium properties, are presented and used to assess the
equilibrium properties of the schemes. It is shown that the proposed schemes
satisfy the expected equilibrium and convergence properties
Analytical and numerical insights into wildfire dynamics: Exploring the advection–diffusion–reaction model
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents a systematic study of a widely used advection–diffusion–reaction wildfire model with non-linear coupling. The importance of single mechanisms is discovered by analysing hierarchical sub-models. Numerical simulations provide further insight into the dynamics. As a result, the influence of wind and model parameters such as the bulk density or the heating value on the wildfire propagation speed and the remaining biomass after the burn are assessed. Linearisation techniques for a reduced model provide surprisingly good estimates for the propagation speed in the full model