Douglas R. Q. Pacheco

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Verified

Douglas verified their affiliation via an institutional email.

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• PhD
• Junior Research Group Leader at RWTH Aachen University

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...

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. On the o...

Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when finite elements are used for the spatial discretisation. This work proposes a simple scalar auxiliary variable...

In finite element methods for incompressible flows, the most popular approach to allow equal-order velocity-pressure pairs are residual-based stabilisations. When using first-order elements, however, the viscous part of the residual cannot be approximated, which often degrades accuracy. For constant viscosity, or by assuming a Lipschitz condition o...

Volume-averaged flow equations model fluid systems with two or more interpenetrating phases, as used in various engineering and science applications. Each fluid obeys its own set of Navier--Stokes equations, and the interphase coupling occurs via mass conservation, drag forces, and a common pressure shared by all phases. Therefore, designing decoup...

This article proposes a framework for estimating temperature fields in food-freezing applications that significantly reduces computational load while ensuring accurate temperature monitoring, representing a promising technological tool for optimizing and controlling food engineering processes. The strategy is based on (i) a mathematical model of a...

Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for incompressible flows, the most popular approach to allow equal-order velocity-pressure interpolation are residu...

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,...

Non-Newtonian fluids are of interest in industrial sectors, biological problems and other natural phenomena. This work proposes rheologically-dependent, spatially and temporally high-order non-residual stabilized finite element formulations. The accuracy of the methods is assessed by tackling highly-convective time-dependent power-law flows. The sp...

This article investigates different implicit-explicit (IMEX) methods for incompressible flows with variable viscosity. The viscosity field may depend on space and time alone or, for example, on velocity gradients. Unlike most previous works on IMEX schemes, which focus on the convective term, we propose also treating parts of the diffusive term exp...

Standard Galerkin methods often perform poorly for problems with low diffusion. In particular for purely convective transport, least-squares (LS) formulations provide a good alternative. While spatial stability is relatively straightforward in a least-squares finite element framework, estimates in time are restricted, in most cases, to one dimension...

Purpose This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem. Design/methodology/approach We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions. Findings Various conforming discretisatio...

Reconstructing the pressure from given flow velocities is a task arising in various applications, and the standard approach uses the Navier–Stokes equations to derive a Poisson problem for the pressure p. That method, however, artificially increases the regularity requirements on both solution and data. In this context, we propose and analyze two a...

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of the diffusive term explicitly to reduce the coupling between the velocity components. We present different, bot...

Finite element tearing and interconnecting (FETI) domain decomposition methods [4] are well-established techniques for the parallel solution of elliptic problems. This is mainly due to their simple implementation and the availability of efficient and robust preconditioning strategies.

Viscoelastic fluids are highly challenging from the rheological standpoint, and their discretization demands robust, efficient numerical solvers. Simulating viscoelastic flows requires combining the Navier–Stokes system with a dynamic tensorial equation, increasing mathematical and computational demands. Hence, fractional‐step methods decoupling th...

Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers’ performance drastically. In this regard, we extend a semi-implicit, p...

For their simplicity and low computational cost, time-stepping schemes decoupling velocity and pressure are highly popular in incompressible flow simulations. When multiple fluids are present, the additional hyperbolic transport equation in the system makes it even more advantageous to compute different flow quantities separately. Most splitting me...

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes...

In incompressible flow problems, the finite element discretization of pressure and velocity can be done through either stable spaces or stabilized pairs. For equal-order stabilized methods with piecewise linear discretization, the classical theory guarantees only linear convergence for the pressure approximation. However, a higher order is often ob...

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single‐point data. Alternatively, relative pressure fields can be reconstructed from imaging‐based velocity measurements by considering viscous and i...

Understanding the mechanical effects of smooth muscle cell (SMC) contraction on the initiation and the propagation of cardiovascular diseases such as aortic dissection is critical. Framed by elastic lamellar sheets in the lamellar unit, there are SMCs in the media with a distinct radial tilt, which indicates their contribution to the radial strengt...

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes...

In various practically relevant incompressible flow problems, such as polymer flow or biomedicalengineering applications, the dependence of fluid viscosity on the local shear rate plays an impor-tant role. Standard techniques using inf-sup stable finite elements lead to saddle-point systemsposing a challenge even for state-of-the-art solvers and pr...

Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are...

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their viscosity depends locally on the flow field. Despite the peculiarities of such models, it is common practice to combine them with numerical techniques conceived for Newtonian fluids, which can bring several iss...

The matter of appropriate boundary conditions for open or truncated outflow regions in internal flow is still focus of discussion and re- search. In most practical applications, one can at best estimate mean pressure values or flow rates at such outlets. In the context of finite element methods, it is known that enforcing mean pressures through the...

Due to simplicity in implementation and data structure, elements with equal‐order interpolation of velocity and pressure are very popular in finite‐element‐based flow simulations. Although such pairs are inf‐sup unstable, various stabilization techniques exist to circumvent that and yield accurate approximations. The most popular one is the pressur...

Computing pressure fields from given flow velocities is a task frequently arising in engineering, biomedical and scientific computing applications. The so-called pressure Poisson equation (PPE) derived from the balance of linear momentum provides an attractive framework for such a task. However, the PPE increases the regularity requirements on the...

Structural and aerodynamic non-linearities can lead to persistent oscillations in aeroelastic systems, which allows the conversion of mechanical energy into electric power. Flexible beams represent an example of structures that can be used as energy harvesters. This work aims to model and analyze the non-linearities induced by the flow-structure in...

For the numerical solution of the pressure Poisson equation, we consider an ultra-weak variational formulation and a related finite element method of Galerkin-Petrov type. While this allows a piecewise constant approximation of the pressure, the test functions have to be sufficiently smooth-in particular, we use modified B-splines of second order t...

Space-time variational methods differ from time-stepping schemes by discretising the whole space-time domain with finite elements. This offers a natural framework for flow problems in moving domains and allows simultaneous parallelisation and adaptivity in space and time. For incompressible flows, the usual approach is to employ the same polynomial...

Panel flutter is an aeroelastic phenomenon that can critically affect aircraft skin in supersonic flight. The majority of works published on this subject treat each skin panel as an isolated structural element. In reality, however, aircraft skin is usually built as large panels stiffened by stringers and frames. Thus, the multiple subpanels sitting...

This study consists of a numerical investigation on the nonlinear flutter oscillations of composite panels on multiple supports (multibay panels) in high supersonic flow. In contrast to what is done in the majority of studies, direct time-domain integration is used here instead of linearized updated mode approximations or modal decomposition techni...