Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow

In this work we are interested in numerical simulations for bedload erosion processes. We present a relaxation solver that we apply to moving dunes test cases in one and two dimensions. In particular we retrieve the so-called anti-dune process that is well described in the experiments. In order to be able to run 2D test cases with reasonable CPU time, we also describe and apply a parallelization procedure by using domain decomposition based on the classical MPI library.Comment: 19 page

Simulating the influences of groundwater on regional geomorphology using a distributed, dynamic, landscape evolution modelling platform

A dynamic landscape evolution modelling platform (CLiDE) is presented that allows a variety of Earth system interactions to be explored under differing environmental forcing factors. Representation of distributed surface and subsurface hydrology within CLiDE is suited to simulation at sub-annual to centennial time-scales. In this study the hydrological components of CLiDE are evaluated against analytical solutions and recorded datasets. The impact of differing groundwater regimes on sediment discharge is examined for a simple, idealised catchment, Sediment discharge is found to be a function of the evolving catchment morphology. Application of CLiDE to the upper Eden Valley catchment, UK, suggests the addition of baseflow-return from groundwater into the fluvial system modifies the total catchment sediment discharge and the spatio-temporal distribution of sediment fluxes during storm events. The occurrence of a storm following a period of appreciable antecedent rainfall is found to increase simulated sediment fluxes

Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods.

This paper is concerned with the numerical approximation of bedload sediment transport due to water evolution. For the hydrodynamical component we consider Shallow Water equations. The morphodynamical component is defined by a continuity equation, which is defined in function of the solid transport discharge. We present several deterministic models, such as Meyer-Peter & Müller, Van Rijn or Grass model. We also present an unified definition for the solid transport discharge, and we compare with Grass model. Both components define a coupled system of equations that can be rewrite as a non-conservative hyperbolic system. To discretize it, we consider finite volume methods with or without flux limiters and high order state reconstructions. Finally we present several tests, where we observe numerically the order of the numerical schemes. Comparisons with analytical solutions and experimental data are also presented

A fast numerical solution to the general mass-conservation equation for solutes and solids in aquatic sediments

Mathematical modeling of species transformations in aquatic sediments is usually based on numerical solutions to the same general one-dimensional mass-conservation equation and is likely to require substantial computation time. In this paper we present a fast numerical solution to this equation. The solution is suited for both single and multi-component models and it is based on an implicit control volume discretization of the general mass-conservation equation. The solution consists of two algorithms, one that decomposes the discretization matrix once and one that subsequently produces multiple solutions with minimal computational effort. A unique feature of these algorithms is that values of boundary conditions can vary as a simulation progresses without requiring new decompositions of the discretization matrix. This feature can reduce computation time significantly relative to commonly used procedures for modeling dynamic systems. Finally, we present four examples in which the numerical solution is applied to specific problems. From these examples guidelines are derived for the discretization in space and time required to obtain precise solutions of the general mass-conservation equation

Dynamics of the motion of a phase change boundary to changes in pressure

Because of the significance of both shallow and deep phase changes to geophysical problems, the dynamical response of a phase change to pressure loading was investigated. It was found that the characteristic behavior of the system may be analyzed in terms of simple parameters of the system by using analytic expressions that apply for the initial part and the final part of the motion of the phase boundary. These expressions are obtained from approximations based on generalizations of Neumann's solution for melting at a constant temperature or from simple physical approximations based on the over-all geometry of the model. The range of applicability of the approximations can be obtained from the approximations themselves. The analytic results compare very favorably with exact numerical solutions. The distribution of heat sources and convective heat transport are shown to be generally of minor importance on the motion of the phase boundary; the effect of convective heat transport can be estimated from the analytic approximation. The important parameters are the latent heat of the phase change and the difference in slope between the Clapeyron curve and the temperature distribution in the earth. In addition, the long-term motion depends primarily on the over-all geometry of the model and the boundary condition at depth. The analytic results indicate the time at which thermal blanketing by sediments becomes important and the effect of the rate of sedimentation on the response of the system; they also define slow and fast sedimentation and secular equilibrium. The effect of isostasy in conjunction with a shallow phase change is shown to be of major importance, and for certain cases the sediment thickness that can accumulate in a sedimentary basin may depend only on the sedimentation rate and not the initial depth of the basin. The analytic results permit a more physical discussion of the problem, since the functional dependence of the solution on the parameters may be seen. In addition, important results for a variety of models can be obtained by relatively simple calculations, without resorting to separate numerical solutions for each model considered

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Modelling alluvial channel dynamics in a river reach dominated by alternate bars

River morphodynamics and sediment transportRiver morphology and morphodynamic

Evaluating river cross section geometry for a hydraulic river routing model : Guadalupe and San Antonio river basins

textA new methodology is presented to construct reliable river channel cross section approximations. These approximations are based on the idea of downstream hydraulic geometry as well as supported by the information collected by the USGS streamflow measurement stations across the study area. A hydraulic river routing model (SPRNT) is run with the newly constructed cross section approximations. Initial conditions for the simulation are estimated based on the steady state solution for the model. Boundary conditions or lateral inflows for the river network are estimated based on the outputs of a Land Surface model: Noah, which provides surface and sub-surface runoff for every catchment area in the San Antonio and Guadalupe river basins. Simulations are compared with observed measurements from the USGS stations.Civil, Architectural, and Environmental Engineerin

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure