# Raimund BürgerUniversidad de Concepción, Concepción, Chile · CI2MA & Departamento de Ingeniería Matemática

Raimund Bürger

Dr. rer. nat.

## About

257

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## Publications

Publications (257)

A model for the spatio-temporal evolution of three biological species in a food chain model consisting of two competitive preys and one predator with intra-specific competition is considered. Besides diffusing, the predator species moves toward higher concentrations of a chemical substance produced by the prey. The prey, in turn, moves away from hi...

El objetivo de esta serie comunicacional es mostrar los modelos matemáticos como herramientas útiles para representar y describir sistemas biológicos. En particular, se busca entregar una mirada sobre las consideraciones generales para tener en cuenta a la hora de modelar sistemas de tratamiento de aguas basados en microalgas y bacterias.

A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is opera...

A non-negligible part of the biological reactions in the activated sludge process for treatment of wastewater takes place in secondary settling tanks that follow biological reactors. It is therefore of interest to develop models of so-called reactive settling that describe the spatial variability of reaction rates caused by the variation of local c...

Cemented paste backfill (CPB) technology is widely used for environmental protection and underground goaf treatment. The influences of solid concentration, coarse aggregates dosage, and cement dosage on the rheological properties and compressive strength of CPB blended with coarse aggregates (CA-CPB) are investigated through three-factor and four-l...

We review some recent advances in the mathematical modelling and numerical simulation of polydisperse suspensions of small particles dispersed in a viscous fluid. Such a mixture contains small particles of multiple species that differ in size or density, and that segregate and form areas of different composition. In one space dimension, common mode...

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We...

Froth flotation is a common unit operation used in mineral processing. It serves to separate valuable mineral particles from worthless gangue particles in finely ground ores. The valuable mineral particles are hydrophobic and attach to bubbles of air injected into the pulp. This creates bubble-particle aggregates that rise to the top of the flotati...

A population balance model is applied to a steel ball mill. Experimental data were obtained for two types of balls with different chemical compositions using a marked ball test in an industrial mill of a recognized cement producer company. The balls were marked since their manufacture by an international ball supplier who guided the entire experime...

Reactive settling is the process of sedimentation of small solid particles in a fluid with simultaneous reactions between the components of the solid and liquid phases. This process is important in sequencing batch reactors (SBRs) in wastewater treatment plants. In that application the particles are biomass (bacteria; activated sludge) and the liqu...

Mathematical models that describe continuous thickening that may be employed for simulation, design and control are usually given as nonlinear, time-dependent partial differential equations that in one space dimension include strongly degenerate convection-diffusion-reaction equations with discontinuous coefficients, and in two or more dimensions,...

The settling velocities of individual particles and particle suspensions are analyzed using a discrete approach. Solid–fluid interaction is studied using the Navier–Stokes and Euler equations of hydrodynamics. Explicit equations for the drag coefficient and settling velocity of spheres and irregularly shaped particles of any size and density are de...

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. Th...

A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is opera...

Classical fifth-order weighted essentially non-oscillatory (WENO) schemes are based on reconstructions from three consecutive second-order polynomials. They give a third-order accurate scheme when two consecutive polynomials are smooth and one is non-smooth. This situation means losing one order of accuracy if compared with a fourth-order scheme. I...

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 4,240,982 cases and 106,544 deaths as of June 30, 2021. This motivates an investigation of the SARS-CoV-2 transmission dynamics at the national and regional level using case incidence data. Mathemati...

Gravity thickening by deep cone thickener is popularly applied in cemented paste backfill, which is essential for tailings management and green mining. To avoid rake bogging, high concentration and high flowability are required for thickened tailings slurry. These properties depend critically on the yield stress of the slurry. The yield stress, in...

These are lecture notes (in Spanish) on conservation laws, which I use for teaching that topic to doctoral students at Universidad de Concepción, Chile.

Informe Técnico (sin publicar), preparado en agosto de 2009. Uno de los pocos documentos de investigación que redacté en español.

Reactive settling is the process of sedimentation of small solid particles in a fluid with simultaneous reactions between the components of the solid and liquid phases. This process is important in sequencing batch reactors (SBRs) in wastewater treatment plants. In that application the particles are biomass (bacteria; activated sludge) and the liqu...

Reactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular importance for the simulation and control of secondary settling tanks (SSTs) in water resource recovery facilities...

The analysis of the double-diffusion model and $\mathbf{H}(\mathrm{div})$-conforming method introduced in [B\"urger, M\'endez, Ruiz-Baier, SINUM (2019), 57:1318--1343] is extended to the time-dependent case. In addition, the efficiency and reliability analysis of residual-based {\it a posteriori} error estimators for the steady, semi-discrete, and...

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (SIAM J. Numer. Anal.54 2951–2973, 2016) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and the...

Soil-based water filtering devices can be described by models of viscous flow in porous media coupled with an advection–diffusion–reaction system modelling the transport of distinct contaminant species within water, and being susceptible to adsorption in the medium that represents soil. Such models are analysed mathematically, and suitable numerica...

Phenomenological growth models (PGMs) provide a framework for characterizing epidemic trajectories, estimating key transmission parameters, gaining insight into the contribution of various transmission pathways, and providing long-term and short-term forecasts. Such models only require a small number of parameters to describe epidemic growth patter...

An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual versi...

A three-dimensional multilayer shallow water approach to study polydisperse sedimentation and sediment transport in a viscous fluid is presented. The fluid is assumed be loaded with finely dispersed solid particles that belong to a finite number of species that differ in density and size. The model formulation allows one to recover the global mass...

Reactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular importance for the simulation and control of secondary settling tanks (SSTs) in water resource recovery facilities...

El correcto modelamiento matemático en conjunto con la simulación numérica ha sido a lo largo de las últimas décadas una poderosa herramienta que ha permitido mejorar el diseño, operación y control de los procesos de concentración de minerales así como los involucrados en las plantas de tratamientos de agua servidas. En la presente comunicación se...

The propagation of a forest fire can be described by a convection-diffusion-reaction problem in two spatial dimensions, where the unknowns are the local temperature and the portion of fuel consumed as functions of spatial position and time. This model can be solved numerically in an efficient way by a linearly implicit-explicit (IMEX) method to dis...

A spatially one-dimensional model of the hydrodynamics of a flotation column is based on one continuous phase, the fluid, and two disperse phases: the aggregates, that is, bubbles with attached hydrophobic valuable particles, and the solid particles that form the gangue. A common feed inlet for slurry mixture and gas is considered and the bubbles a...

This study revises the non-local macroscopic pedestrian flow model proposed in [R. M. Colombo, M. Garavello, and M. Le ́cureux-Mercier. A class of nonlocal models for pedestrian traffic. Math. Models Methods Appl. Sci., 22(4):1150023, 2012] to account for anisotropic interactions and the presence of walls or other obstacles in the walking domain. W...

Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-l...

High-efficiency flocculation and settling is required for solid–liquid separation in cemented paste backfill, which is one of the best approaches for tailings management and green mining. The optimization of flocculation and settling parameters of tailings slurry was carried out by response surface methodology (RSM) with Box–Behnken design. The sol...

Flotation is a separation process where particles or droplets are removed from a suspension with the aid of floating gas bubbles. Applications include dissolved air flotation (DAF) in industrial wastewater treatment and column froth flotation (CFF) in wastewater treatment and mineral processing. One-dimensional models of flotation have been limited...

A macroscopic model is introduced for simulating the sedimentation–consolidation of solid particles in an incompressible fluid under the effect of gravity and in the presence of a slowly rotating arm assisting the removal of sediment on the bottom of clarifier–thickener units. The governing model is an initial–boundary value problem for the Navier–...

A reaction–diffusion system is formulated to describe three interacting species within the Hastings–Powell (HP) food chain structure with chemotaxis produced by three chemicals. We construct a finite volume (FV) scheme for this system, and in combination with the non-negativity and a priori estimates for the discrete solution, the existence of a di...

The well-known Lighthill-Whitham-Richards (LWR) kinematic model of traffic flow models the evolution of the local density of cars by a non-linear scalar conservation law. The transition between free and congested flow regimes can be described by a flux or velocity function that has a discontinuity at a determined density. A numerical scheme to hand...

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer. Anal. 54 (2016) 2951--2973] is proposed. The treatment is extended to include also the transient case. Appropri...

The continuous unit operation of flotation is extensively used in mineral processing, wastewater treatment and other applications for selectively separating hydrophobic particles (or droplets) from hydrophilic ones, where both are suspended in a viscous fluid. Within a flotation column, the hydrophobic particles are attached to gas bubbles that are...

An entropy conservative (EC) numerical flux for the multiclass Lighthill-Whitham-Richards (MCLWR) kinematic traffic model based on the general framework by Tadmor [E. Tadmor, The numerical viscosity of entropy stable schemes for systems of conservation laws, I, Math. Comput., 49 (1987), pp. 91-103] is proposed. The approach exploits the existence o...

Common smoothness indicators used in Weighted Essentially Non-Oscillatory (WENO) reconstructions (Jiang and Shu in J Comput Phys 126:202–228, 1996) have quadratic cost with respect to the order. A set of novel smoothness indicators with linear cost of computation with respect to the order is presented. These smoothness indicators can be used in the...

A stationary Navier-Stokes-Brinkman problem coupled to a system of advection-diffusion equations serves as a model for so-called double-diffusive viscous flow in porous media in which both heat and a solute within the fluid phase are subject to transport and diffusion. The solv-ability analysis of these governing equations results as a combination...

Phenomenological models are particularly useful for characterizing epidemic trajectories because they often offer a simple mathematical form defined through ordinary differential equations (ODEs) that in many cases can be solved explicitly. Such models avoid the description of biological mechanisms that may be difficult to identify, are based on a...

The numerical solution of nonlinear convection-diffusion equations with nonlocal flux by explicit finite difference methods is costly due to the local spatial convolution within the convective numerical flux and the disadvantageous Courant-Friedrichs-Lewy (CFL)condition caused by the diffusion term. More efficient numerical methods are obtained by...

Entropy stable schemes for the numerical solution of initial value problems of nonlinear, possibly strongly degenerate systems of convection–diffusion equations were recently proposed in Jerez and Parés's study. These schemes extend the theoretical framework of Tadmor's study to convection–diffusion systems. They arise from entropy conservative sch...

A multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and form areas of different composition. In addition, the...

Nonlinear convection–diffusion equations with nonlocal flux and possibly degenerate diffusion arise in various contexts including interacting gases, porous media flows, and collective behavior in biology. Their numerical solution by an explicit finite difference method is costly due to the necessity of discretizing a local spatial convolution for e...

A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure is based on the construction of a global average weight using the whole set of Jiang–Shu smoothness indicator...

A spatio-temporal eco-epidemiological model is formulated by combining an available non-spatial model for predator-prey dynamics with infected prey [D. Greenhalgh and M. Haque, Math. Meth. Appl. Sci., 30 (2007), 911–929] with a spatio-temporal susceptible-infective (SI)-type epidemic model of pattern formation due to diffusion [G.-Q. Sun, Nonlinear...

Polymer flooding in petroleum reservoir engineering can be described by a Brinkman‐based model of flow in porous media coupled to a non‐strictly hyperbolic system of conservation laws for multiple components that form the aqueous phase. The coupled flow‐transport problem is discretized by coupling an H(div)‐conforming discontinuous Galerkin (DG) me...

Strongly degenerate parabolic convection–diffusion equations arise as governing equations in a number of applications such as traffic flow with driver reaction and anticipation distance and sedimentation of solid–liquid suspensions in mineral processing and wastewater treatment. In these applications several parameters that define the convective fl...

A general and realistic population balance model is applied to a ceramic ball mill. The experimental data are
obtained for three differently sized balls. The mill is operated 500 h with silica sand during 8 cycles. After each
cycle, the mill is stopped to measure the ball wear to obtain the kinetics wear equations. It turns out that the
wear law fo...

The hindered-settling velocity function for the modelling, simulation and control of secondary settling tanks can be determined from batch tests. The conventional method is to measure the velocity of the descending sludge-supernatant interface (sludge blanket) as the change in height over time in a vessel with constant cross-sectional area. Each su...

Flotation is a unit operation extensively used in the recovery of valuable minerals in mineral processing and related applications. Essential insight to the hydrodynamics of a flotation column can be obtained by studying just two phases: gas and fluid. To this end, the approach based on the drift-flux theory, proposed in similar form by several aut...

A method is presented for the identification of non-convex flux functions of hyperbolic scalar conservation laws that model sedimentation of solid particles in a liquid. While all previous identification methods are based on data obtained from settling tests in cylindrical vessels, the novel approach is based on the richer solution behaviour produc...

Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of diff...

The Aw–Rascle–Zhang traffic model, a model of sedimentation, and other applications lead to nonlinear \(2 \times 2\) systems of conservation laws that are governed by a single scalar system velocity. Such systems are of the Temple class since rarefaction wave curves and Hugoniot curves coincide. Moreover, one characteristic field is genuinely nonli...

Polymer flooding is an important stage of enhanced oil recovery in petroleum reservoir engineering. A model of this process is based on the study of multicomponent viscous flow in porous media with adsorption. This model can be expressed as a Brinkman-based model of flow in porous media coupled to a nonstrictly hyperbolic system of conservation law...

Techniques for the efficient approximate solution of systems of convection-diffusion partial differential equations modelling the sedimentation of droplets of different sizes in a viscous fluid are introduced. These techniques comprise the use of Polynomial Viscosity Matrix (PVM) methods for the convective numerical fluxes and implicit treatment of...

Abstract. Techniques for the efficient approximate solution of systems of convection-diffusion partial differential equations modelling the sedimentation of droplets of different sizes in a viscous fluid are introduced. These techniques comprise the use of Polynomial Viscosity Matrix (PVM) methods for the convective numerical fluxes and implicit tr...

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear m...

A quasi-one-dimensional model of the process of continuous sedimentation in clarifier-thickeners (settlers) with variable cross-sectional area is presented. The partial differential equation (PDE) model extends the settler model advanced in [R. Bürger, S. Diehl, S. Farås, I. Nopens, E. Torfs, Water Sci. Tech. 68 (2013) 192–208], which assumes a con...

The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in gen...

The vehicular traffic on an infinite or circular highway can be represented by the diffusively corrected Lighthill-Whitham-Richards (DCLWR) model, but the uncertain knowledge requires to deal with uncertain model parameters.
The stochastic Galerkin based methods allow to transform a randomly perturbed PDE to a high dimensional deterministic system,...

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the under- lying strongly degenerate parabolic, nonlinear...

In [E. Torfs et al., Water Sci. Tech., 75 (2017), 539-551] a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The e...

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511–524]. Both subpopulations are assumed to...