arXiv subjects

Matteo Parsani

Publications and source records attributed to Matteo Parsani.

At least 19 recordsLinked to original sources

arXiv2026

Entropy-stable moving-wall boundary conditions for the ALE formulation of the compressible Navier-Stokes equations

We present a high-order entropy-stable framework for the compressible Euler and Navier-Stokes equations on moving domains. The space-time mapping describing the domain motion is recast in an arbitrary Lagrangian Eulerian (ALE) formulation, in which the physical inviscid fluxes and the contributions induced by mesh motion are treated in a unified manner. At the continuous level, we prove that the proposed moving-wall boundary conditions are entropy conservative for the Euler equations and entropy stable for the Navier-Stokes equations. The no-slip condition is formulated in terms of the velocity relative to the moving wall, yielding a bounded inviscid contribution to the entropy balance, while the viscous terms contribute only entropy dissipation. Using diagonal norm summation-by-parts (SBP) operators together with appropriate numerical fluxes, these properties are extended to the semi-discrete formulation, resulting in nonlinear stability in the $L^2$ sense. The accuracy, robustness, and scalability of the proposed method are demonstrated in practice through an extensive set of numerical experiments, ranging from canonical two-dimensional verification cases to large-scale turbulent and supersonic simulations involving moving boundaries and fluid-structure interaction. The results confirm the suitability of high-order entropy-stable schemes for complex moving-domain problems across a broad range of flow regimes and multiphysics applications. Because the analysis relies on the SBP property rather than on a particular discretization, the framework naturally extends to a broad class of methods based on diagonal-norm SBP operators, including finite volume, finite element, and flux reconstruction schemes.

math.NA↗

arXiv2026

ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries

Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate. We introduce the ambient-domain extension Fourier neural operator (ADEx-FNO), a deterministic framework that incorporates geometry without modifying the defining Fourier-operator layers. Each physical domain is embedded in a fixed ambient hypercube and represented by a signed distance function. Inputs and solution fields are deterministically extended to the ambient domain, transferred to a common, potentially nonuniform rectilinear latent grid, processed by the FNO, then interpolated to an independently chosen target discretization and restricted to the physical domain. All geometry-transfer operations lie outside the optimization procedure and require no trainable graph, point-cloud, deformation, or geometry-decoding modules. ADEx-FNO achieves relative l2 errors of 0.32%-0.77% on held-out smooth-domain nonlinear Poisson and advection-reaction-diffusion problems in 2D and 3D, and is also evaluated on unseen nonsmooth geometries. A single ADEx-FNO inference is then used to initialize conventional CFD solvers. For all 29 converged 2D and 3D RANS cases, pseudo-time iterations decrease, with mean reductions of 44.17% and 43.03%, respectively, with comparable gains across three mesh resolutions. URANS cases reduce post-window physical-time advances by 18.52%-27.51%. In transfer from 2D URANS training data to DNS at different Mach and Reynolds numbers, the bootstrap interval decreases by 23.47%-48.21%, depending on the target statistic. In all CFD tests, ADEx-FNO provides only the initial field; the governing-equation solver controls the subsequent solution, while physical or statistical consistency is assessed separately from computational savings.

math.NA↗

arXiv2026

Influence of plume activity on thermal convection in a rectangular cell

We present three-dimensional direct numerical simulations of turbulent Rayleigh-B\'enard convection in a closed rectangular box whose width $L_y$ and length $L_x$ are 0.8 and 2.4 times the height $H$, respectively. The Rayleigh number $Ra$ varies from $10^5$ to $10^{10}$, and the Prandtl number is unity. The advantages of the present configuration are: (a) A relatively stable unidirectional large-scale circulation, consisting of two counter-rotating rolls, fills the cell and fixes the thermal plume ejection- and shear-dominated regions, in contrast to those in closed cylindrical cells. (b) The regions of plume ejection are essentially independent of the sidewalls so that their autonomous existence can be studied. This is because there is some space, or "fetch", for the velocity and thermal boundary layers to develop along the length. (c) This geometry allows one to study the influence of locally thin and thick boundary layers (which follow larger or smaller plume activity) on the scaling of convection properties. In regions of larger plume activity (defined by an incessant movement of plumes), the temperature fluctuation as well as the normalised thermal and viscous dissipation rates decay more slowly with $Ra$ than in regions of lower activity. Both viscous and thermal boundary layers thin down rapidly with increasing distance from the plume ejection region. The local thicknesses of both boundary layers decline more rapidly with $Ra$ in the ejection region than in regions of impact and shear, where they are similar to each other. Despite these details, the global heat transport laws are practically the same as those in other configurations of low to moderate aspect ratios.

physics.flu-dyn↗

arXiv2025

HelioFill: Diffusion-Based Model for EUV Reconstruction of the Solar Farside

The loss of STEREO-B in 2014 created a persistent blind spot in Extreme Ultraviolet (EUV) imaging of the solar farside. We present HelioFill, to the authors' knowledge, the first denoising-diffusion inpainting model that restores full-Sun EUV coverage by synthesizing the STEREO-B sector from Earth-side (SDO) and STEREO-A views. Trained on full-Sun maps from 2011-2014 (when SDO+STEREO-A+B provided 360 degrees coverage), HelioFill couples a latent diffusion backbone with domain-specific additions: spectral gating, confidence weighting, and auxiliary regularizers, to produce operationally suitable 304 Angstrom reconstructions. On held-out data, the model preserves the observed hemisphere with mean SSIM 0.871 and mean PSNR 25.56 dB, while reconstructing the masked hemisphere with mean SSIM 0.801 and mean PSNR 17.41 dB and reducing boundary error by approximately 21 percent (Seam L2) compared to a state-of-the-art diffusion inpainting model. The generated maps maintain cross-limb continuity and coronal morphology (loops, active regions, and coronal-hole boundaries), supporting synoptic products and cleaner inner-boundary conditions for coronal/heliospheric models. By filling observational gaps with observationally consistent EUV emission, HelioFill maintains continuity of full-Sun monitoring and complements helioseismic farside detections, illustrating how diffusion models can extend the effective utility of existing solar imaging assets for space-weather operations.

astro-ph.SR↗

arXiv2025

VeMo: A Lightweight Data-Driven Approach to Model Vehicle Dynamics

Developing a dynamic model for a high-performance vehicle is a complex problem that requires extensive structural information about the system under analysis. This information is often unavailable to those who did not design the vehicle and represents a typical issue in autonomous driving applications, which are frequently developed on top of existing vehicles; therefore, vehicle models are developed under conditions of information scarcity. This paper proposes a lightweight encoder-decoder model based on Gate Recurrent Unit layers to correlate the vehicle's future state with its past states, measured onboard, and control actions the driver performs. The results demonstrate that the model achieves a maximum mean relative error below 2.6% in extreme dynamic conditions. It also shows good robustness when subject to noisy input data across the interested frequency components. Furthermore, being entirely data-driven and free from physical constraints, the model exhibits physical consistency in the output signals, such as longitudinal and lateral accelerations, yaw rate, and the vehicle's longitudinal velocity.

cs.RO↗

arXiv2025

Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence

Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases have not been explored in detail and limits the optimal utilization of new high-performance computing systems. In this work, the effect of reduced precision is studied using four diverse computational fluid dynamics (CFD) solvers (two incompressible, Neko and Simson, and two compressible, PadeLibs and SSDC) using four test cases: turbulent channel flow at Retau = 550 and higher, forced transition in a channel, flow over a cylinder at ReD = 3900, and compressible flow over a wing section at Rec = 50000. We observe that the flow physics are remarkably robust with respect to reduction in lower floating-point precision, and that often other forms of uncertainty, due to for example time averaging, often have a much larger impact on the computed result. Our results indicate that different terms in the Navier-Stokes equations can be computed to a lower floating-point accuracy without affecting the results. In particular, standard IEEE single precision can be used effectively for the entirety of the simulation, showing no significant discrepancies from double-precision results across the solvers and cases considered. Potential pitfalls are also discussed.

physics.flu-dyn↗

arXiv2024

Entropy conservative and entropy stable solid wall boundary conditions for the resistive magnetohydrodynamic equations

We present a novel technique for imposing non-linear entropy conservative and entropy stable wall boundary conditions for the resistive magnetohydrodynamic equations in the presence of an adiabatic wall or a wall with a prescribed heat entropy flow, addressing three scenarios: electrically insulating walls, thin walls with finite conductivity, and perfectly conducting walls. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts, and simultaneous-approximation-term operators. Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions is coupled with an entropy-conservative or entropy-stable discrete interior operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation operators (mass lumped nodal discontinuous Galerkin operators) on high-order unstructured grids are used to demonstrate the new procedure's accuracy, robustness, and efficacy for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional flows. The procedure described is compatible with any diagonal-norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, nodal and modal discontinuous Galerkin, and flux reconstruction schemes.

math.NA↗

arXiv2024

Fully-discrete provably Lyapunov consistent discretizations for convection-diffusion-reaction PDE systems

Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space. Understanding and preserving their stability properties in numerical simulation is crucial for accurate predictions, system analysis, and decision-making. This work presents a comprehensive framework for constructing fully discrete Lyapunov-consistent discretizations of any order for convection-diffusion-reaction models. We introduce a systematic methodology for constructing discretizations that mimic the stability analysis of the continuous model using Lyapunov's direct method. The spatial algorithms are based on collocated discontinuous Galerkin methods with the summation-by-parts property and the simultaneous approximation terms approach for imposing interface coupling and boundary conditions. Relaxation Runge-Kutta schemes are used to integrate in time and achieve fully discrete Lyapunov consistency. To verify the properties of the new schemes, we numerically solve a system of convection-diffusion-reaction partial differential equations governing the dynamic evolution of monomer and dimer concentrations during the dimerization process. Numerical results demonstrated the accuracy and consistency of the proposed discretizations. The new framework can enable further advancements in the analysis, control, and understanding of general convection-diffusion-reaction systems.

math.NA↗

arXiv2024

On the relevance of lift force modelling in turbulent wall flows with small inertial particles

In particle-laden turbulent wall flows, lift forces can influence the near-wall turbulence. This has been recently observed in particle-resolved simulations, which, however, are too expensive to be used in upscaled models. Instead, point-particle simulations have been the method of choice to simulate the dynamics of these flows during the last decades. While this approach is simpler, cheaper, and physically sound for small inertial particles in turbulence, some issues remain. In the present work, we address challenges associated with lift force modelling in turbulent wall flows and the impact of lift forces in the near-wall flow. We performed direct numerical simulations (DNS) of small inertial point particles in turbulent channel flow for fixed Stokes number and mass loading while varying the particle size. Our results show that the particle dynamics in the buffer region, causing the apparent particle-to-fluid slip velocity to vanish, raises major challenges for accurately modelling lift forces. While our results confirm that lift forces have little influence on particle dynamics for sufficiently small particle sizes, for inner-scaled diameters of order one and beyond, lift forces become quite important near the wall. The different particle dynamics under lift forces results in the modulation of streamwise momentum transport in the near-wall region. We analyze this lift-induced turbulence modulation for different lift force models, and the results indicate that realistic models are critical for particle-modelled simulations to correctly predict turbulence modulation by particles in the near-wall region.

physics.flu-dyn↗

arXiv2023

A hybrid discrete exterior calculus and finite difference method for anelastic convection in spherical shells

The present work develops, verifies, and benchmarks a hybrid discrete exterior calculus and finite difference (DEC-FD) method for density-stratified thermal convection in spherical shells. Discrete exterior calculus (DEC) is notable for its coordinate independence and structure preservation properties. The hybrid DEC-FD method for Boussinesq convection has been developed by Mantravadi et al. (Mantravadi, B., Jagad, P., & Samtaney, R. (2023). A hybrid discrete exterior calculus and finite difference method for Boussinesq convection in spherical shells. Journal of Computational Physics, 491, 112397). Motivated by astrophysics problems, we extend this method assuming anelastic convection, which retains density stratification; this has been widely used for decades to understand thermal convection in stars and giant planets. In the present work, the governing equations are splitted into surface and radial components and discrete anelastic equations are derived by replacing spherical surface operators with DEC and radial operators with FD operators. The novel feature of this work is the discretization of anelastic equations with the DEC-FD method and the assessment of a hybrid solver for density-stratified thermal convection in spherical shells. The discretized anelastic equations are verified using the method of manufactured solution (MMS). We performed a series of three-dimensional convection simulations in a spherical shell geometry and examined the effect of density ratio on convective flow structures and energy dynamics. The present observations are in agreement with the benchmark models.

physics.flu-dyn↗

arXiv2023

Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package

We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD (https://github.com/MathEXLab/PySPOD) library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py (https://mpi4py.readthedocs.io/en/stable/). An extensive performance evaluation of the parallel package is provided, including strong and weak scalability analyses. The open-source library allows the analysis of large datasets of interest across the scientific community. Here, we present applications in fluid dynamics and geophysics, that are extremely difficult (if not impossible) to achieve without a parallel algorithm. This work opens the path toward modal analyses of big quasi-stationary data, helping to uncover new unexplored spatio-temporal patterns.

physics.comp-ph↗

arXiv2022

On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics

We study temporal step size control of explicit Runge-Kutta methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations. We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number. Our numerical examples show that error-based step size control is easy to use, robust, and efficient, e.g., for (initial) transient periods, complex geometries, nonlinear shock capturing approaches, and schemes that use nonlinear entropy projections. We demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases, the open source Julia packages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.

math.NA↗

arXiv2021

Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows

Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Sv\"{a}rd (Physica A: Statistical Mechanics and its Applications, 2018). and its spatial discretization based on entropy stable collocated discontinuous Galerkin operators with the summation-by-parts property for unstructured grids. A set of viscous test cases of increasing complexity are simulated using both the Eulerian and the classic compressible Navier-Stokes models. The numerical results obtained with the two models are compared, and differences and similarities are then highlighted.

math.NA↗

arXiv2021

A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions

When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume (FV) schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. In this paper, we propose a rotated characteristic decomposition technique which requires only one-time decomposition for multi-dimensional reconstructions. The rotated direction depends only on the gradient of a specific physical quantity which is cheap to calculate. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume (WENO-FV) scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique.

math.NA↗

arXiv2021

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.

math.NA↗

arXiv2021

A class of high-order weighted compact central schemes for solving hyperbolic conservation laws

We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation element and solution element (CESE) scheme. On every cell, the solution is approximated by a Pth order polynomial of which all the DOFs are stored and updated separately. The cell average is updated by a classical finite volume scheme which is constructed based on space-time staggered meshes such that the fluxes are continuous across the interfaces of the adjacent control volumes and, therefore, the local Riemann problem is bypassed. The kth order spatial derivatives are updated by a central difference of (k-1)th order spatial derivatives at cell vertices. All the space-time information is calculated by the Cauchy-Kovalewski procedure. By doing so, the schemes are able to achieve arbitrarily uniform spacetime high order on a super-compact stencil with only one explicit time step. In order to capture discontinuities without spurious oscillations, a weighted essentially non-oscillatory (WENO) type limiter is tailor-made for the schemes. The limiter preserves the compactness and high order accuracy of the schemes. The accuracy, robustness, and efficiency of the schemes are verified by several numerical examples of scalar conservation laws and the compressible Euler equations.

math.NA↗

arXiv2020

Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations

Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for finitely many convex functionals (entropies) and apply the resulting methods to the compressible Euler and Navier-Stokes equations. Based on the unstructured $hp$-adaptive SSDC framework of entropy conservative or dissipative semidiscretizations using summation-by-parts and simultaneous-approximation-term operators, we develop the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily high-order accurate in space and time. We demonstrate the accuracy and the robustness of the fully-discrete explicit locally entropy-stable solver for a set of test cases of increasing complexity.

math.NA↗

arXiv2019

On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the algorithmic level, hardware compatibility and efficiency are of paramount importance in determining viability at exascale and beyond. However, equally important (if not more so) is algorithmic robustness with minimal user intervention, which becomes progressively more challenging to achieve as problem size and physics complexity increase. We numerically show that low and high order entropy stable discontinuous spatial discretizations based on summation-by-part operators and simultaneous-approximation-terms technique provides an essential step toward a truly enabling technology in terms of reliability and robustness for both under-resolved turbulent flow simulations and flows with discontinuities.

math.NA↗