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1. Full Text A high‐order parallel Eulerian‐Lagrangian algorithm for advection‐diffusion problems on unstructured meshes
by Tavelli, Maurizio and Boscheri, Walter
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 11/2019, Volume 91, Issue 7, pp. 332 - 347
Summary In this paper, we present a high‐order discontinuous Galerkin Eulerian‐Lagrangian method for the solution of advection‐diffusion problems on staggered... 
advection | diffusion | Eulerian‐Lagrangian | MPI | discontinuous Galerkin | semi‐implicit | transport equation | unstructured mesh | MULTIPLY-UPSTREAM | VELOCITY RECONSTRUCTION | PHYSICS, FLUIDS & PLASMAS | DISCONTINUOUS GALERKIN METHOD | MODEL | ACCURACY | FREE-SURFACE FLOWS | SCHEME | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | Eulerian-Lagrangian | semi-implicit | Algorithms | Stability | Computer simulation | Computational fluid dynamics | Fluid flow | Dimensions | Mapping | Velocity distribution | Velocity | Equations | Sound velocity | Incompressible flow | Advection | Message passing | Discretization | Mathematical analysis | Efficiency | Computer applications | Parallel processing | Scaling | Galerkin method | Reference systems | Particle trajectories | Diffusion
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2. Full Text A pressure-based semi-implicit space–time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier–Stokes equations at all Mach numbers
by Tavelli, Maurizio and Dumbser, Michael
Journal of Computational Physics, ISSN 0021-9991, 07/2017, Volume 341, pp. 341 - 376
We propose a new arbitrary high order accurate semi-implicit space–time discontinuous Galerkin (DG) method for the solution of the two and three dimensional... 
All Mach number flows | Pressure-based semi-implicit space–time discontinuous Galerkin scheme | Compressible Navier–Stokes equations | Staggered unstructured meshes | High order of accuracy in space and time | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | Compressible Navier Stokes equations | SHALLOW-WATER EQUATIONS | GODUNOV-TYPE SCHEMES | FREE-SURFACE | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Pressure-based semi-implicit space time discontinuous Galerkin scheme | DYNAMIC GRID MOTION | VISCOUS INCOMPRESSIBLE-FLOW | FINITE-ELEMENT-METHOD | HYPERBOLIC CONSERVATION-LAWS | DRIVEN CAVITY FLOW | Fluid dynamics | Energy conservation | Statistics | Methods | Force and energy | Mathematics - Numerical Analysis
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3. Arbitrary high order accurate space–time discontinuous Galerkin finite element schemes on staggered unstructured meshes for linear elasticity
by Maurizio Tavelli and Michael Dumbser
Journal of Computational Physics, ISSN 0021-9991, 08/2018, Volume 366, p. 386
In this paper we propose a new high order accurate space–time discontinuous Galerkin (DG) finite element scheme for the solution of the linear elastic wave... 
Stresses | Degrees of freedom | Propagation | Wave equations | Elasticity | Velocity distribution | Elastic waves | Velocity | Matrix methods | Finite element method | Accuracy | Discretization | Mathematical analysis | Galerkin method | Finite element analysis | Iterative methods
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4. Full Text Arbitrary high order accurate space–time discontinuous Galerkin finite element schemes on staggered unstructured meshes for linear elasticity
by Tavelli, Maurizio and Dumbser, Michael
Journal of Computational Physics, ISSN 0021-9991, 08/2018, Volume 366, pp. 386 - 414
In this paper we propose a new high order accurate space–time discontinuous Galerkin (DG) finite element scheme for the solution of the linear elastic wave... 
Energy stability | High order schemes | Staggered unstructured meshes | Large time steps | Linear elasticity | Space–time discontinuous Galerkin methods | HETEROGENEOUS MEDIA | 1ST-ORDER HYPERBOLIC FORMULATION | WAVE-PROPAGATION PROBLEMS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | STEPPING METHODS | FREE-SURFACE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Space-time discontinuous Galerkin methods | NAVIER-STOKES EQUATIONS | STABILITY ANALYSIS | ADER SCHEMES | DYNAMIC GRID MOTION | Mathematics - Numerical Analysis
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5. A pressure-based semi-implicit space–time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier–Stokes equations at all Mach numbers
by Maurizio Tavelli and Michael Dumbser
Journal of Computational Physics, ISSN 0021-9991, 07/2017, Volume 341, p. 341
We propose a new arbitrary high order accurate semi-implicit space–time discontinuous Galerkin (DG) method for the solution of the two and three dimensional... 
Compressibility | Enthalpy | Fluid flow | Eulers equations | Finite volume method | Velocity distribution | High Mach number | Heat flux | Operators (mathematics) | Thermodynamics | Discretization | Mathematical analysis | Energy conservation | Polynomials | Kinetic energy | Mach number | Conservation equations | Computer simulation | Preprocessing | Computational fluid dynamics | Numerical methods | Navier Stokes equations | Studies | Incompressible flow | Shock waves | Equations of state | Galerkin method | Kinetics | Heat transfer | Navier-Stokes equations
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6. Full Text A staggered semi-implicit discontinuous Galerkin method for the two dimensional incompressible Navier–Stokes equations
by Tavelli, Maurizio and Dumbser, Michael
Applied Mathematics and Computation, ISSN 0096-3003, 12/2014, Volume 248, pp. 70 - 92
In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional... 
Curved isoparametric elements | Semi-implicit discontinuous Galerkin schemes | Incompressible Navier–Stokes equations | High order staggered finite element schemes | Staggered unstructured triangular meshes | Incompressible Navier-Stokes equations | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | FREE-SURFACE HYDRODYNAMICS | HYPERBOLIC SYSTEMS | BACKWARD-FACING STEP | HIGH-RESOLUTION METHODS | FINITE-ELEMENT APPROXIMATION | SHALLOW-WATER EQUATIONS | REYNOLDS-NUMBER | UNSTRUCTURED MESHES | SPATIAL DISCRETIZATION | Fluid dynamics | Methods | Computation | Mathematical analysis | Mathematical models | Polynomials | Two dimensional | Galerkin methods | Curved | Navier-Stokes equations
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7. Full Text A high order semi-implicit discontinuous Galerkin method for the two dimensional shallow water equations on staggered unstructured meshes
by Tavelli, Maurizio and Dumbser, Michael
Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 234, pp. 623 - 644
A well-balanced, spatially arbitrary high order accurate semi-implicit discontinuous Galerkin scheme is presented for the numerical solution of the two... 
Shallow water equations | Curved isoparametric elements | Non-orthogonal grids | Large time steps | High order semi-implicit discontinuous Galerkin schemes | Staggered unstructured triangular meshes | Galerkin schemes | MATHEMATICS, APPLIED | FREE-SURFACE HYDRODYNAMICS | HIGH-RESOLUTION METHODS | WELL-BALANCED SCHEME | MAXWELLS EQUATIONS | NONCONSERVATIVE HYPERBOLIC SYSTEMS | SOURCE TERMS | NAVIER-STOKES EQUATIONS | VOLUME SCHEMES | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD | High order semi-implicit discontinuous | Preprocessing | Computation | Mathematical analysis | Mathematical models | Polynomials | Galerkin methods | Finite difference method
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8. Full Text A staggered space–time discontinuous Galerkin method for the incompressible Navier–Stokes equations on two-dimensional triangular meshes
by Tavelli, Maurizio and Dumbser, Michael
Computers and Fluids, ISSN 0045-7930, 09/2015, Volume 119, pp. 235 - 249
In this paper we propose a novel arbitrary high order accurate semi-implicit space–time discontinuous Galerkin method for the solution of the two dimensional... 
Staggered unstructured meshes | Incompressible Navier–Stokes equations | Space–time pressure correction method | Isoparametric finite elements for curved boundaries | Semi-implicit space–time discontinuous Galerkin scheme | High order accuracy in space and time | Space-time pressure correction method | Incompressible Navier-Stokes equations | Semi-implicit space-time discontinuous Galerkin scheme | Semi-implicit space-time discontinuous | CONVECTION-DIFFUSION PROBLEMS | COMPRESSIBLE FLOWS | FREE-SURFACE HYDRODYNAMICS | HYPERBOLIC SYSTEMS | HIGH-RESOLUTION METHODS | SHALLOW-WATER EQUATIONS | Galerkin scheme | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DYNAMIC GRID MOTION | UNSTRUCTURED MESHES | SPATIAL DISCRETIZATION | FINITE-ELEMENT-METHOD | Fluid dynamics | Methods | Algorithms | Incompressible flow | Approximation | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Two dimensional | Galerkin methods | Navier-Stokes equations
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9. Full Text A staggered space–time discontinuous Galerkin method for the three-dimensional incompressible Navier–Stokes equations on unstructured tetrahedral meshes
by Tavelli, Maurizio and Dumbser, Michael
Journal of Computational Physics, ISSN 0021-9991, 08/2016, Volume 319, pp. 294 - 323
In this paper we propose a novel arbitrary high order accurate semi-implicit discontinuous Galerkin method for the solution of the three-dimensional... 
High order schemes | Space–time pressure correction algorithm | Staggered unstructured meshes | Incompressible Navier–Stokes equations in 3D | Space–time discontinuous Galerkin finite element schemes | Space-time pressure correction algorithm | Space-time discontinuous Galerkin finite element schemes | Incompressible Navier-Stokes equations in 3D | CONVECTION-DIFFUSION PROBLEMS | COMPRESSIBLE FLOWS | LID-DRIVEN CAVITY | SEMIIMPLICIT METHOD | BACKWARD-FACING STEP | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMIC GRID MOTION | Incompressible Navier-Stokes equations in | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD | Fluid dynamics | Methods | Algorithms | Finite element method | Computational fluid dynamics | Mathematical analysis | Mathematical models | Polynomials | Galerkin methods | Three dimensional | Navier-Stokes equations | Mathematics - Numerical Analysis
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10. Full Text A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography
by Tavelli, Maurizio and Dumbser, Michael and Charrier, Dominic Etienne and Rannabauer, Leonhard and Weinzierl, Tobias and Bader, Michael
Journal of Computational Physics, ISSN 0021-9991, 06/2019, Volume 386, pp. 158 - 189
In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by... 
Diffuse interface method (DIM) | High order schemes | Linear elasticity equations for seismic wave propagation | Adaptive mesh refinement (AMR) | Complex geometries | Discontinuous Galerkin schemes | 1ST-ORDER HYPERBOLIC FORMULATION | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FREE-SURFACE | FINITE-VOLUME METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | TO-DETONATION TRANSITION | ORDER ADER SCHEMES | SPECTRAL ELEMENT METHOD | CONSERVATION-LAWS | STAGGERED UNSTRUCTURED MESHES | Wave propagation | Seismic waves | Seismology | Analysis | High resolution | Compressibility | Propagation | Elasticity | Mapping | Elastic waves | Characteristic functions | Complexity | Finite element method | Energy dissipation | Topography | Eigenvalues | Mathematical models | Mesh generation | Free surfaces | Discontinuity | Wave equations | Coordinates | Geophysics | Boundary conditions | Thickness | Problems | Unity | Computation | Galerkin method
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11. Full Text A divergence‐free semi‐implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics
by Dumbser, M and Balsara, D.S and Tavelli, M and Fambri, F
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 01/2019, Volume 89, Issue 1-2, pp. 16 - 42
Summary In this paper, we present a novel pressure‐based semi‐implicit finite volume solver for the equations of compressible ideal, viscous, and resistive... 
ideal magnetohydrodynamics | viscous and resistive MHD | all Mach number flow solver | divergence‐free | finite volume schemes | semi‐implicit | compressible low Mach number flows | general equation of state | pressure‐based method | pressure-based method | semi-implicit | divergence-free | HLLC RIEMANN SOLVER | TANG VORTEX SYSTEM | THERMODYNAMIC PROPERTIES | PHYSICS, FLUIDS & PLASMAS | 1ST-ORDER HYPERBOLIC FORMULATION | GODUNOV-TYPE SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ORDER ADER SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Viscosity | Magnetohydrodynamics | Divergence | Compressibility | Methodology | Fluid flow | Finite volume method | Energy | Mathematical analysis | Solvers | Evolution | Mach number | Computational fluid dynamics | Momentum equation | Curl (vectors) | Dimensions | Momentum | Pressure | Velocity | Equations | Internal energy | Incompressible flow | Simulation | Energy equation | Volume | Newton methods | Computer applications | Scaling | Magnetic fields | Computing time | Riemann solver | Linear functions
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