Abstract : Hyperbolic PDE systems naturally appear in many real-world applications, particularly in geophysical flow models. They are of essential importance for understanding natural phenomena and for their prediction.
This mini-symposium focuses on geophysical flows with a particular interest in the shallow water framework and related applications such as sediment transport, tsunami hazards, and viscoplastic flows.
The objective will be to discuss and presents new trends in computational and numerical methods for shallow flows and their applications.
[01506] Monotonicity-preserving interpolation in multilevel schemes for balance laws
Format : Talk at Waseda University
Author(s) :
Antonio Baeza (University of Valencia, Spain)
Rosa Donat (University of Valencia)
Anna Martínez-Gavara (University of Valencia)
Abstract : This work deals with the problem of developing cost-effective multilevel schemes for balance laws, in particular for the shallow water equations in 1D and 2D. We focus on the application of monotonicity-preserving interpolatory techniques as a tool for the recursive computation of the numerical divergence in the different grids, which is a key step on multilevel schemes. Numerical tests confirm that this technique leads to a more robust multilevel code while improving its efficiency.
[01433] Entropy-stable, positivity-preserving and well-balanced Godunov-type schemes for multidimensional shallow-water system
Format : Talk at Waseda University
Author(s) :
Agnes Chan (CEA Cesta - Université de Bordeaux)
Gérard Gallice (CEA Cesta)
Raphaël Loubère (Université de Bordeaux)
Pierre-Henri Maire (CEA Cesta)
Alessia Del Grosso (CEA Cesta - Université de Bordeaux)
Abstract : An entropy stable, positivity preserving Godunov-type scheme for multidimensional hyperbolic systems of conservation laws on unstructured grids was presented by Gallice et al. in 2022. A specific feature of their Riemann solver is coupling all cells in the vicinity of the current one, making their solver no longer 1D across one edge.
We extend their work to handle source terms, specifically for shallow water equations. The scheme we obtain is well-balanced in 1D and 2D.
[01511] Numerical solution of a system of conservation laws with discontinuous flux modelling flotation with sedimentation
Format : Talk at Waseda University
Author(s) :
Raimund Bürger (Universidad de Concepción)
Stefan Diehl (Lund University)
Carmen Marti Raga (Universitat de València)
Yolanda Vásquez (Universidad de Concepción)
Abstract : Froth flotation is a unit operation used in mineral processing to separate valuable mineral particles from worthless gangue particles in finely ground ores. In this talk, we will present a model for froth flotation, including the drainage of liquid that occurs at the top of the column. We will detail the construction of steady-state solutions and present some results that show the ability of the model to capture steady operation of the flotation device.
[01508] Implicit and IMEX Lagrange Projection schemes for Ripa model
Format : Talk at Waseda University
Author(s) :
Celia Caballero Cárdenas (Universidad de Málaga)
Manuel Jesús Castro Díaz (Universidad de Málaga)
Tomas Morales de Luna (Universidad de Málaga)
María Luz Muñoz-Ruiz (Universidad de Málaga)
Abstract : We consider the one-dimensional system of shallow equations with horizontal temperature gradients, i.e., the Ripa system. We present a numerical approximation of this system based on a Lagrange-Projection type finite volume scheme. We shall consider fully implicit and implicit-explicit versions of the scheme for the Lagrangian step, while the Projection step will always be done explicitly. Several numerical experiments are included in order to illustrate the good behavior of the proposed schemes.
[01400] Vertical discretizations of Euler systems and application to bedload problems
Format : Talk at Waseda University
Author(s) :
José Garres-Díaz (Universidad de Córdoba)
Tomas Morales de Luna (Universidad de Malaga)
Cipriano Escalante Sanchez (Universidad de Málaga)
Manuel Castro Díaz (Universidad de Málaga)
Abstract : Shallow water type systems are very popular in numerical simulation of geophysical flows, mainly due to their low computational cost. However, these systems share an important drawback: the vertical information of the flow is lost. In this talk, we present a general framework for vertical discretizations of free-surface Euler system, that generalizes the moment and multilayer techniques. It is called multilayer-moment approach. Several tests are presented, pointing out advantages/disadvantages of each approach, and their efficiency.
[01507] Numerical methods for viscoplastic flows : balancing precision and acceleration
Format : Talk at Waseda University
Author(s) :
Clément Berger (UMPA CNRS UMR 5669, ENS de Lyon)
Abstract : We consider here equations for yield stress flows formulated as variational inequalities. The reason is that it allows the best numerical computation of the interfaces between fluid zones and rigid zones. In this talk, we compare multiple optimization methods, from proximal algorithms to second-order cone programming. The compromise between precision and speed differs from one method to another. We will also comment on each associated convergence criteria.
[01504] Digital Twins (DT) on geophysical extreme hazards. Using Tsunami-HySEA numerical model as DT for tsunami hazards.
Format : Talk at Waseda University
Author(s) :
Jose Manuel Gonzalez-Vida (Dpt. Applied Mathematics. University of Malaga)
Jorge Macías (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
Manuel J. Castro (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
Alex González (Dpt. Mathematical Analysis, Statistics and Applied Mathematics)
Abstract : A Digital Twin (DT) for GEOphysical extremes (DT-GEO) is an European project that aims to analyse and forecast the impact of tsunamis, earthquakes, volcanoes, and anthropogenic seismicity. This work address tsunami hazard phenomena to conduct precise data-informed early warning systems, forecasts, and tsunami-hazard assessments across multiple time scales.
[01513] Novel schemes for overdetermined thermodynamically compatible hyperbolic systems
Format : Online Talk on Zoom
Author(s) :
Saray Busto (Universidade de Vigo)
Michael Dumbser (University of Trento)
Abstract : We introduce a novel efficient general class of thermodynamically compatible, HTC, semi-discrete finite volume and discontinuous Galerkin schemes for overdetermined HTC systems. The approach is based on the discretization of the entropy being the total energy conservation a direct consequence of the HTC discretization. The obtained schemes are provably marginally stable in the energy norm, satisfy a discrete entropy inequality by construction and are assessed using classical benchmarks for turbulent shallow water and compressible flows.