Juan Manzanero

• PhD. in Aerospace Engineering
• Professor (Assistant) at Universidad Politécnica de Madrid

We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flo...

A novel free–energy stable discontinuous Galerkin method is developed for the Cahn–Hilliard equation with non–conforming elements. This work focuses on dynamic polynomial adaptation (p–refinement) and constitutes an extension of the method developed by Manzanero et al. in Journal of Computational Physics 403:109072, 2020, which makes use of the sum...

We present a Computational Fluid Dynamics (CFD)–based methodology for the modeling of erosion and corrosion in hydrocarbon pipes. The novelty of this work is the use of a high–order Discontinuous Galerkin Spectral Element Method (DGSEM) approximation of the incompressible Navier–Stokes/Cahn–Hilliard model for the CFD simulation. This technique perm...

We present a high–order discontinuous Galerkin (DG) discretization for the three–phase Cahn–Hilliard model of [Boyer, F., & Lapuerta, C. (2006). Study of a three component Cahn–Hilliard flow model]. In this model, consistency is ensured with an additional term in the chemical free–energy. The model considered in this work includes a wall boundary c...

This paper presents a space-time approximate diffusion-dispersion analysis of high-order, finite volume Upwind Central (UWC) and Weighted Essentially Non-Oscillatory (WENO) schemes. We perform a thorough study of the numerical errors to find a-priori guidelines for the computation of under-resolved turbulent flows. In particular, we study the 3-rd,...

In this work we introduce the development of a three--phase incompressible Navier--Stokes/Cahn--Hilliard numerical method to simulate three--phase flows, present in many industrial operations. The numerical method is then applied to successfully solve oil transport problems, such as those found in the oil and gas industry. The three--phase model ad...

We present a provably stable discontinuous Galerkin spectral element method for the incompressible Navier–Stokes equations with artificial compressibility and variable density. Stability proofs, which include boundary conditions, that follow a continuous entropy analysis are provided. We define a mathematical entropy function that combines the trad...

We present a new closure model for Large Eddy Simulation to introduce dissipation in under–resolved turbulent simulation using discontinuous Galerkin (DG) schemes applied to the compressible Navier–Stokes equations. The development of the method is based on a thorough analysis of the numerical dissipation mechanisms in DG schemes. In particular, we...

We develop an entropy–stable two–phase incompressible Navier–Stokes/Cahn–Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn–Hilliard equation as the phase field method, a skew–symmetric form of the momentum equation, and an artificial compressibility method to compute the pressure. We design the model so that it satis...

We present implicit Large Eddy Simulations for NACA0012 airfoils at various Reynolds numbers ( Re = 1 × 10 ⁴ , Re = 1 × 10 ⁵ and Re = 1 × 10 ⁶ ) and Angles of Attack (0 ∘ ≤ AoA ≤ 10 ∘ ) using two discontinuous Galerkin formulations. On the one hand, we use a compressible solver based on a nodal DGSEM formulation and supplemented with a stabilising...

We present a multiphase model for incompressible flows of two immiscible fluids. Our model solves one shared set of incompressible Navier–Stokes equations for the two phase flow and an additional equation: the Cahn–Hilliard equation, for the evolution of the two fluids distribution. The introduced model is discretised in space using a high-order Di...

We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum equation, and an artificial compressibility method to compute the pressure. We design the model so that it sat...

We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn–Hilliard equation that satisfies the summation–by–parts simultaneous–approximation–term (SBP–SAT) property. The latter permits us to show that the discrete free–energy is bounded, and as a result, the scheme is provably stable. The scheme and the stability proof are presented for ge...

We present a provably stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes equations with artificial compressibility and variable density. Stability proofs, which include boundary conditions, that follow a continuous entropy analysis are provided. We define a mathematical entropy function that combines the trad...

We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn-Hilliard equation that satisfies the summation-by-parts simultaneous-approximation-term (SBP-SAT) property. The latter permits us to show that the discrete free-energy is bounded, and as a result, the scheme is provably stable. The scheme and the stability proof are presented for ge...

High-order discontinuous Galerkin methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the order also increases the computational cost. Several techniques have been introduced in the...

High-order DG methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the order also increases the computational cost. Several techniques have been introduced in the past to reduce this...

We analyse instabilities due to aliasing errors when solving one dimensional non-constant advection speed equations and discuss means to alleviate these types of errors when using high order discontinuous Galerkin (DG) schemes. First, we compare analytical bounds for the continuous and discrete version of the PDEs. Whilst traditional $L^2$ norm ene...

We analyse numerical errors (dissipation and dispersion) introduced by the discretisation of inviscid and viscous terms in energy stable discontinuous Galerkin methods. First, we analyse these methods using a linear von Neumann analysis (for a linear advection-diffusion equation) to characterise their properties in wave-number space. Second, we val...

In the discontinuous Galerkin (DG) community, several formulations have been proposed to solve PDEs involving second-order spatial derivatives (e.g. elliptic problems). In this paper, we show that, when the discretisation is restricted to the usage of Gauss–Lobatto points, there are important similarities between two common choices: the Bassi-Rebay...

This paper presents an extended version of von Neumann stability analysis to study dispersion and dissipation errors in nonconstant coefficient advection equations. This approach is used to analyze the behavior of discontinuous Galerkin (DG) discretizations, including the influence of polynomial order, number of elements, and choice of quadrature p...