
Luca BonaventuraPolitecnico di Milano | Polimi · Department of Mathematics "Francesco Brioschi"
Luca Bonaventura
PhD
Theoretical analysis of fluid dynamics models and dynamical systems.
About
190
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Introduction
After training in mathematical physics and probability, I have worked for 30 years as applied mathematician developing numerical methods for computational fluid dynamics, weather prediction and other environmental applications. Presently, I am going back to studying more theoretical topics in mathematical physics and dynamical systems.
Additional affiliations
Education
April 1997 - March 1998
January 1990 - December 1994
November 1984 - November 1989
Publications
Publications (190)
This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent gravity currents, performed by means of a Discontinuous Galerkin (DG) Finite Element method. In particular, a DG-LES approach in which the filter operation is built in the numerical discretization has been employed, similarly to VMS approaches. Num...
We present an adaptive discretization approach for model equations typical of numerical weather prediction, which combines the semi-Lagrangian technique with the TR-BDF2 semi-implicit time discretization method and with a DG spatial discretization with variable and adaptive element degree. The resulting method has full second order accuracy in time...
We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. In order to ac...
We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already emp...
A numerical method for the two-dimensional, incompressible Navier– Stokes equations in vorticity–streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the...
We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in state of the art computational fluid dynamics codes, in combination with high-order methods, such as the Finite...
Lecture notes of a PhD course on numerical methods for Ordinary Differential Equations
We systematically validate the static local mesh refinement capabilities of a recently proposed implicit–explicit discontinuous Galerkin scheme implemented in the framework of the deal.II library. Non‐conforming meshes are employed in atmospheric flow simulations to increase the resolution around complex orography. The proposed approach is fully ma...
We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly scalable thanks to its data locality properties, and on a second order Implicit-Explicit Runge-Kutta (IMEX-RK) me...
We present an approach for the efficient implementation of self- adjusting multi-rate Runge-Kutta methods and we extend the previously available stability analyses of these methods to the case of an arbitrary number of sub-steps for the active components. We propose a physically motivated model problem that can be used to assess the stability of di...
We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in earlier numerical methods, whereas they are employed nowadays to an increasing extent in combination with high-order methods, such as the Finite Element Method (FEM) and the Spectral Element...
We analyze schemes based on a general Implicit-Explicit (IMEX) time discretization for the compressible Euler equations of gas dynamics, showing that they are asymptotic-preserving(AP) in the low Mach number limit. The analysis is carried out for a general equation of state(EOS). We consider both a single asymptotic length scale and two length scal...
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal .II library. Non-conforming meshes are employed in atmospheric flow simulations to increase the resolution around complex orography. A number of numerical experiments based on classical benchmarks w...
We perform a quantitative assessment of different strategies to compute the contribution due to surface tension in incompressible two-phase flows using a conservative level set (CLS) method. More specifically, we compare classical approaches, such as the direct computation of the curvature from the level set or the Laplace-Beltrami operator, with a...
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the interface. We analyze the evolution equations for a set of geometrical quantities that characterize the interface in t...
We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based on a h-adaptive Discontinuous Galerkin spatial discretization and on a second order Additive Runge Kutta IMEX...
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the interface. We analyze the evolution equations for a set of geometrical quantities that characterize the interface in t...
We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture. Currently, the calculation of the phase-space stability region of hadron storage rings is performed through d...
https://authors.elsevier.com/a/1h4BYMMTPor9N
We assess the performance of two domain-specific languages included in the GridTools ecosystem as tools for implementing a high-order Discontinuous Galerkin discretization of the shallow water equations. Also equations in spherical geometry are considered, thus providing a blueprint for the application of domain-specific languages to the developmen...
We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture. Currently, the calculation of the phase-space stability region of hadron storage rings is performed through d...
We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equations describing non-ideal gases with general cubic equation of state and Stiffened-Gas EOS. The method is based on an h-adaptive Discontinuous Galerkin spatial discretization and on an Additive Runge Kutta IMEX method for time discretization. It is spec...
We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based on an h−adaptive Discontinuous Galerkin spatial discretization and on a second order Additive Runge Kutta IMEX...
We introduce economical versions of standard implicit ODE solvers that are specifically tailored for the efficient and accurate simulation of neural networks. The specific versions of the ODE solvers proposed here, allow to achieve a significant increase in the efficiency of network simulations, by reducing the size of the algebraic system being so...
We propose an efficient, accurate and robust implicit solver for the incompressible Navier‐Stokes equations, based on a DG spatial discretization and on the TR‐BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely...
Presentation for HYP2022 conference
Presentation at the ESCO 2022 conference Pilsen June 15 2022
We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equation with general equation of state. The method, which is based on an $h-$adaptive Discontinuos Galerkin spatial discretization and on an Additive Runge Kutta IMEX method for time discretization, is tailored for low Mach number applications and allows to...
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test...
Dynamic polynomial adaptivity in Local Discontinuous Galerkin framework applied to Large Eddy Simulation
Final presentation of the ESCAPE-2 WP1 activity
This work is based on the seminar titled ``Resiliency in Numerical Algorithm Design for Extreme Scale Simulations'' held March 1-6, 2020 at Schloss Dagstuhl, that was attended by all the authors.
Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronou...
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore, also for the variable density equations, a variable number of layers can be used, so as to achieve greater flexib...
We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely...
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. The proposed method allows to use large time steps, while avoiding the solution of large linear syste...
We present a numerical model of soil erosion at the basin scale that allows one to describe surface runoff without a priori identifying drainage zones, river beds and other water bodies. The model is based on robust and unconditionally stable numerical techniques and guarantees mass conservation and positivity of the surface and subsurface water la...
In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity, accounting for the scale invariance and relative scale of these data. We show that the method can be used in a block sequential Gaussia...
The application of the TR-BDF2 method to second order problems typical of structural mechanics and seismic engineering is discussed. A reformulation of this method is presented, that only requires the solution of algebraic systems of size equal to the number of displacement degrees of freedom. A linear analysis and numerical experiments on relevant...
This deliverable complements the list of dwarfs inherited from the original ESCAPE project with novel concepts that include parallel implementation of high order discontinuous finite elements (DG) in spherical geometry, advanced linear solvers to support semi-implicit time discretizations, fault-tolerant versions of linear solvers already employed...
In this work we describe a first version of the simulation tool developed within the SMART-SED project. The two main components of the SMART-SED model consist in a data preprocessing tool and in a robust numerical solver, which does not require a priori identification of river beds and other surface run-off areas, thus being especially useful to pr...
Progress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations f...
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of hyperbolic-parabolic equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test...
This work is based on the seminar titled ``Resiliency in Numerical Algorithm Design for Extreme Scale Simulations'' held March 1-6, 2020 at Schloss Dagstuhl, that was attended by all the authors. Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronous...
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to overcome the numerical difficulties arising from higher order derivative terms, especially in the context of h...
We present a first dynamically adaptive test of a physically based p-refinement criterion for DG-LES approaches recently proposed by the authors and applied so far to static adaptation only. The results, albeit preliminary, are encouraging and show that, also in the dynamically adaptive case, the proposed criterion allows to reduce significantly th...
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore, also for the variable density equations, a variable number of layers can be used, so as to achieve greater flexib...
The application of the TR-BDF2 method to second order problems typical of structural mechanics and seismic engineering is discussed. A reformulation of this method is presented, that only requires the solution of algebraic systems of size equal to the number of displacement degrees of freedom. A linear analysis and numerical experiments on relevant...
In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscale...
Sediment yield from mountain basins and solid transport in rivers are widely studied and still represent a major issue when dealing with hydrogeological hazard. The correct determination of flooding scenarios involving huge amounts of debris also has implications for cities and human infrastructure safety. However, studies focused on catchment scal...
The computation of analytic and numerical beam based quantities are derived for full 3D representation of the quadrupoles magnetic field, which can be computed by finite element code or measured. The impact of this more accurate description of the non homogeneity of the field is estimated on beam based observables and non linear correctors strength...
We investigate the possibility of reducing the computational burden of LES configurations by employing locally and dynamically adaptive polynomial degrees in the framework of a high order DG method. A degree adaptation technique especially featured to be effective for LES applications, that was previously developed by the authors and tested in the...
We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and accuracy of IGA approaches wit...
We present results of three-dimensional direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent gravity currents with a discontinuous Galerkin finite elements method. In particular, we consider the lock-exchange test case as a benchmark for gravity currents. Since, to the best of our knowledge, non-Boussinesq three-dimensio...
Numerical weather and climate prediction rates as one of the scientific appli-
cations whose accuracy improvements greatly depend on the growth of the
available computing power. As the number of cores in top computing facil-
ities pushes into the millions, increasing average frequency of hardware and
software failures forces users to review their a...
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to overcome the numerical difficulties and the severe time step restrictions arising from higher order terms. The...
We propose a semi-Lagrangian method for the numerical solution of the incompressible Navier–Stokes equations. The method is based on the Chorin–Temam fractional step projection method, combined with a fully semi-Lagrangian scheme to approximate both advective and diffusive terms in the momentum equation. A standard finite element method is used ins...
We review recent results in the development of a class of accurate, efficient, high order, dynamically p-adaptive Discontinuous Galerkin methods for geophysical flows. The proposed methods are able to capture phenomena at very different spatial scales, while minimizing the computational cost by means of a dynamical degree adaptation procedure and o...
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. Standard interpolation procedures are used for the space discretization on structured and unstructured me...
We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and accuracy of IGA approaches wit...
We show the distinctive potential advantages of a self adjusting multirate method based on diagonally implicit solvers for the robust time discretization of partial differential equations. The properties of the specific ODE methods considered are reviewed, with special focus on the TR-BDF2 solver. A general expression for the stability function of...