arXiv subjects

Douglas Pacheco

Publications and source records attributed to Douglas Pacheco.

4 recordsLinked to original sources

arXiv2026

A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics

Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation for simulating incompressible flows from laminar to turbulent regimes. The method is embedded in an incremental pressure-correction fractional-step framework and employs a minimal set of stabilization terms, yielding a unified discretization that (i) allows equal-order velocity--pressure interpolation and (ii) provides robust control of convection-dominated dynamics in complex three-dimensional settings. Orthogonal projections are a key ingredient and ensure that the non-residual, term-by-term structure induces dissipation through dynamic subscales suitable for turbulent simulations. The methodology is validated on large-scale external-aerodynamics configurations, including the Ahmed body at Re $ = 7.68\times 10^{5}$ for multiple slant angles, using unstructured tetrahedral meshes ranging from 3 to 40 million elements. Applicability is further demonstrated on a realistic Formula~1 configuration at $U_\infty=56~\mathrm{m/s}$ (201.6~km/h), corresponding to Re $ \approx 10^{6}$. The results show that the proposed stabilized pressure-segregated formulation remains robust at scale and captures key separated-flow features and coherent wake organization. Pointwise velocity and pressure spectra provide an a posteriori consistency indicator, exhibiting finite frequency ranges compatible with inertial-subrange reference slopes in the resolved band and supporting dissipation control in under-resolved regimes within a unified stabilized finite element framework.

physics.flu-dyn↗

arXiv2025

A fully segregated and unconditionally stable IMEX scheme for dispersed multiphase flows

Euler--Euler or volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled via drag forces and a shared pressure. Monolithic solvers can therefore be very expensive and difficult to implement, so there is great computational appeal for decoupled methods. However, splitting the subproblems requires treating the coupling terms (pressure and drag) explicitly, which must be done carefully to avoid time-step restrictions. In this context, we derive a new first-order pressure-correction method based on the incompressibility of the mean velocity field, combined with an explicit treatment of the drag forces. Furthermore, both the convective and viscous terms are treated semi-implicitly. This gives us an implicit-explicit (IMEX) method that is very robust not only due to its unconditional energy stability, but also because it does not require any type of fixed-point iterations. Each time step has only linear, scalar transport equations and a single pressure Poisson problem as building blocks. We rigorously prove temporal stability without any CFL-like conditions, and the theory is confirmed through two-phase numerical examples.

math.NA↗

arXiv2024

A fast food-freezing temperature estimation framework using optimally located sensors

This article presents and assesses a framework for estimating temperature fields in real time for food-freezing applications, significantly reducing computational load while ensuring accurate temperature monitoring, which represents a promising technological tool for optimizing and controlling food engineering processes. The strategy is based on (i) a mathematical model of a convection-dominated problem coupling thermal convection and turbulence, and (ii) a least-squares approach for solving the inverse data assimilation problem, regularized by projecting the governing dynamics onto a reduced-order model (ROM). The unsteady freezing process considers a salmon slice in a freezer cabinet, modeled with temperature-dependent thermophysical properties. The forward problem is approximated using a third-order WENO finite volume solver, including an optimized second-order backward scheme for time discretization. We employ our data assimilation framework to reconstruct the temperature field based on a limited number of sensors and to estimate temperature distributions within frozen food. Sensor placement is optimized using a novel greedy algorithm, which maximizes the observability of the reduced-order dynamics for a fixed set of sensors. The proposed approach allows efficient extrapolation from external sensor measurements to the internal temperature of the food under realistic turbulent flow conditions, which is crucial for maintaining food quality.

math.NA↗

arXiv2024

Unconditionally stable, linearised IMEX schemes for incompressible flows with variable density

For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in time some methods previously analysed for variable viscosity and constant density. We present three new schemes, both monolithic and fractional-step. All of them share the methodological novelty that the viscous term is treated in an implicit-explicit (IMEX) fashion, which allows decoupling the velocity components. Unconditional temporal stability is proved for all three variants. Furthermore, the system to solve at each time step is linear, thus avoiding the costly solution of nonlinear problems even if the viscosity follows a non-Newtonian rheological law. Our presentation is restricted to the semi-discrete case, only considering the time discretisation. In this way, the results herein can be applied to any spatial discretisation. We validate our theory through numerical experiments considering finite element methods in space. The tests range from simple manufactured solutions to complex two-phase viscoplastic flows.

math.NA↗