139 citations · 698 across the 17 of their papers we have counts for
17 papers
Structure preserving hybrid Finite Volume Finite Element method for compressible MHD
Francesco Fambri, Eric Sonnendrücker
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration stra…
Mass, momentum and energy preserving FEEC and broken-FEEC schemes for the incompressible Navier-Stokes equations
Valentin Carlier, Martin Campos Pinto, Francesco Fambri
In this article we propose two finite element schemes for the Navier-Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and a…
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
F. Fambri, E. Zampa, S. Busto +4
We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 sp…
A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics
Francesco Fambri
In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magnetohydrodynamics (MHD) ba…
A new causal general relativistic formulation for dissipative continuum fluid and solid mechanics and its solution with high-order ADER schemes
Ilya Peshkov, Evgeniy Romenski, Francesco Fambri +1
We present a unified causal general relativistic formulation of dissipative and non-dissipative continuum mechanics. The presented theory is the first general relativistic theory t…
On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
Michael Dumbser, Francesco Fambri, Elena Gaburro +1
In this paper we propose an extension of the generalized Lagrangian multiplier method (GLM) of Munz et al. (JCP 2000, JCP 2002), which was originally conceived for the numerical so…
ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems
Anne Reinarz, Dominic E. Charrier, Michael Bader +13
ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typicall…
Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine
Michael Dumbser, Francesco Fambri, Maurizio Tavelli +2
In this paper we discuss a new and very efficient implementation of high order accurate ADER discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel su…
An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels
Francesco Fambri, Michael Dumbser, Vincenzo Casulli
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arte…
A divergence-free semi-implicit finite volume scheme for ideal, viscous and resistive magnetohydrodynamics
Michael Dumbser, Dinshaw S. Balsara, Maurizio Tavelli +1
In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The ne…
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
Francesco Fambri, Michael Dumbser, Sven Köppel +2
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper…
Semi-implicit discontinuous Galerkin methods for the incompressible Navier-Stokes equations on adaptive staggered Cartesian grids
Francesco Fambri, Michael Dumbser
In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-ti…
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations: spectral analysis and computational results
M. Dumbser, F. Fambri, I. Furci +3
The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) nu…
Space-time adaptive ADER-DG schemes for dissipative flows: compressible Navier-Stokes and resistive MHD equations
Francesco Fambri, Michael Dumbser, Olindo Zanotti
This paper presents an arbitrary h.o. accurate ADER DG method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent PDE for co…
Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids
Francesco Fambri, Michael Dumbser
In this paper two new families of arbitrary high order accurate spectral DG finite element methods are derived on staggered Cartesian grids for the solution of the inc.NS equations…
Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
Olindo Zanotti, Francesco Fambri, Michael Dumbser
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER d…
Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Olindo Zanotti, Francesco Fambri, Michael Dumbser +1
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conser…