In this work we propose a very high-order compressible finite volume scheme with a posteriori stabilization for the computation of multi-component two-phase flow with phase change. It is based on finite volume approach using moving least squares (MLS) reproducing kernels for high order reconstruction of the Riemann states. Increased robustness is achieved by using the multi-dimensional optimal order detection (MOOD) method to get a high-accurate and low-dissipation scheme while maintaining boundedness and preventing numerical oscillations at interfaces and strong gradient zones. The properties of the proposed framework are demonstrated on classical test problems starting with convergence order verification on simple scalar advection test cases. More complex shock and more stringent tube tests with various water, steam and air concentration are then simulated and compared with available references in the literature. Finally, the ability of the proposed approach to compute multi-component flows with phase change is illustrated with the simulation of a liquid oxygen jet in gaseous hydrogen.

The accurate and efficient numerical solution of the Riemann problem is the basis of Godunov-type schemes. Approximate Riemann solvers are widely used for their efficiency, although they exhibit inaccuracies and instabilities in challenging regimes such as strong rarefactions or near-vacuum conditions. This work explores the use of deep neural networks (NNs) to address these limitations. We present two distinct data-driven frameworks: first, a NN-based solver trained to predict the exact solution of the Riemann problem, and second, a high-performance hybrid scheme. The hybrid approach uses the standard Harten-Lax-van Leer-contact (HLLC) Riemann solver as the main solver, enhanced with a computationally inexpensive, physics-based detector that identifies interfaces where the HLLC solution is likely to be inaccurate or to fail. At these interfaces, the scheme selectively uses the pretrained NN to ensure a more accurate solution. Through a series of benchmark tests, we show that the NN solver accurately reproduces the exact solution of the Riemann problem, but at a significant computational cost. In contrast, the proposed hybrid solver achieves a comparable level of accuracy to the NN solver, while it requires nearly the same computational cost as the standard HLLC solver.

In this study, a historical review of the Finite Element Method (FEM) and Molecular Dynamics (MD), widely used at the macro and nanoscale respectively is presented, emphasizing the actual parallelisms between their development and applications. After this historical introduction, where certain similarities between both methods are pointed out, different FEM-like methods are analyzed and compared as for first order analysis of structures at the nanoscale. Firstly, the Structural Mechanics (SM) approach is analyzed, where it is assumed that the use of Euler Bernoulli beam elements is equivalent to working directly from the force field. On the other hand, the Molecular Element Method (MEM), which provides the stiffness matrices directly from the potentials, is analyzed. Several analytical static cases are studied for the validation and comparison of both methods. Finally, it is shown that, other branch of methods such as Elastic Network Models (ENM) can be viewed as a particular sub-case of the MEM, or as truss-type finite elements. As an example, the analysis of SARS-CoV2 spikes vibrations is included, comparing with both experimental results and continuous models.

Surface tension plays a crucial role in determining the interfacial behavior between partially miscible fluid systems, and affects the overall dynamics of phase transition processes. Accurate modeling of surface tension is crucial for understanding and predicting various phase transition phenomena, such as capillary-driven flows, droplet formation, and interfacial dynamics. Cubic equations of state (EoS), such as the van der Waals (vdW) model, incorporate two corrective terms to account for intermolecular interactions. These terms improve the predictions of the equation of state at high pressures and low temperatures, where intermolecular forces become significant; however they also affect to the effective surface tension when the EoS is used in combination with diffuse-interface models of multiphase systems. The ability to capture the correct surface tension is essential in pore-scale models flow through permeable media, particularly in capillary-dominated flow regimes. For typical geological or industrial pore sizes the effective surface tension obtained using standard equations of state may be several orders of magnitude larger than the physical value, which greatly affects the accuracy and physical fidelity of the simulations. In this work we present a methodology that allows diffuse-interface numerical methods to reproduce the physical surface tension in pore-scale simulations of multiphase flow. The proposed methodology is applied to the simulation of interfacial processes at arbitrary length scales while honoring the physical surface tension driving capillary phenomena.

In this paper we present a formulation, denoted as the Molecular Element Method, that allows, given a certain force field, the possibility of performing a first order analysis as is common in structural mechanics. The stiffness matrices have been obtained in an exact way, without the need to resort to any assumptions other than those used to define the force field. Obtaining these matrices analytically allows the exploitation of algorithms and techniques typical of finite elements, being able to perform both static and vibration mode analysis independently of the molecular geometry. In this aspect, the formulation has been validated by studying the frequencies and vibration modes of several molecules, comparing with both theoretical and experimental results. Values of the modulus of elasticity of both graphene sheets and carbon nanotubes have also been obtained in accordance with the values present in the literature. Finally, the formulation shows its potential allowing to obtain the flexural wave dispersion in nanotubes compared to results using Tersoff-Brenner potentials and non-local elasticity models.

Given the small wavelengths and wide range of frequencies of the acoustic waves involved in Aeroacoustics problems, the use of very accurate, low-dissipative numerical schemes is the only valid option to accurately capture these phenomena. However, as the order of the scheme increases, the computational time also increases. In this work, we propose a new high-order flux reconstruction in the framework of finite volume (FV) schemes for linear problems. In particular, it is applied to solve the Linearized Euler Equations, which are widely used in the field of Computational Aeroacoustics. This new reconstruction is very efficient and well suited in the context of very high-order FV schemes, where the computation of high-order flux integrals are needed at cell edges/faces. Different benchmark test cases are carried out to analyze the accuracy and the efficiency of the proposed flux reconstruction. The proposed methodology preserves the accuracy while the computational time relatively reduces drastically as the order increases.

Machine learning (ML) is becoming a powerful tool in Computational Fluid Dynamics (CFD) to enhance the accuracy, efficiency, and automation of simulations. Currently, in the design of shock-capturing methods, there is still a heavy reliance on the expertise and scientific knowledge of each author, particularly in nonlinear components such as smoothness indicators and weighting functions. ML has the potential to reduce this dependency, since by leveraging large datasets, they can learn intricate patterns and make accurate predictions of these functions. In this work we present a neural network that compute the weighting functions in the WENO5 scheme. The proposed WENO5-NN scheme generalizes well for different resolutions, and in most of the cases tested, it outperforms the classical WENO5-JS scheme.

We present a new methodology to statistically determine the net present value (NPV) and internal rate of return (IRR) as financial estimators of shale gas investments. Our method allows us to forecast, in a fully probabilistic setting, financial performance risk and to understand the importance of the different factors that impact investment. The methodology developed in this study combines, through Monte Carlo simulation, the computational modeling of gas production from shale gas wells with a stochastic simulation of gas price as a geometric Brownian motion (GMB). To illustrate the methodology’s validity, we apply it to an analysis of investments in shale gas wells. Our results show that gas price volatility is a key variable in the performance of an investment of this type, in such a way that at high volatilities, the potential return on an investment in shale gas increases significantly, but so do the risks of economic loss. This finding is consistent with the history of shale gas operations in which huge investment successes coexist with unexpected investment failures.

We consider the moving least squares method to solve compressible two-phase water-water vapor flow with surface tension. A diffuse interface model based on the Navier-Stokes and Korteweg equations is coupled with a suitable system of state equations that allows for a more realistic estimation of the pressure jump across the liquid-vapor interface as a function of temperature. We propose a simple formulation for computing the capillarity coefficient lambda$$ \lambda $$ based on the surface tension and the thickness of the diffuse interface. A convergence analysis using pressure jump in the test case of static bubble is conducted to verify our solver. We present several numerical test cases that illustrate the ability of our model to reproduce qualitatively and quantitatively the effects of surface tension on cavitation bubbles in general situations.

Mesh-based and particle methods were conceived as two different discretization strategies to solve partial differential equations. In the last two decades computational methods have diversified and a myriad of hybrid formulations that combine elements of these two approaches have been developed to solve Computational fluid dynamics problems. In this work we present a review about the meshless-FV family of methods, an analysis is carried out showing that the MLS-SPH-ALE method can be considered as a general formulation from which a set of particle-based methods can be recovered. Moreover, we show the relations between the MLS-SPH-ALE method and the finite volume method. The MLS-SPH-ALE method is a versatile particle-based method that was developed to circumvent the consistency issues of particle methods caused by the use of the kernel approximation. The MLS-SPH-ALE method is developed from the differential equation in ALE form using the partition unity property which is automatically fulfilled by the Moving Least Squares approximation.

In this paper we propose a new arbitrary-order Finite Volume method for the numerical solution of the Euler and Navier-Stokes equations on unstructured grids. Arbitrary order is achieved using a modified Moving Least Squares reconstruction, which preserves the mean values of the conservative variables. Hence, the proposed scheme changes the traditional error functional of the MLS reconstruction in order to compare the cell-averaged values. Several benchmark problems are used to assess the proposed scheme’s accuracy and performance, to show that arbitrary order of convergence can be achieved. Furthermore, the proposed method is applied to the numerical solution of the Navier-Stokes equations and its ability to simulate turbulent flows is verified.

This work developed a kinetic model for the epoxidation of used cooking oils (UCOs) via Prileschajew reaction with peracetic acid formed in situ. Such models, that have been not reported, are required for process design to assess feasibility of exploitation of UCOs as feedstock in the production of value-added oleochemical epoxides. The study evaluated the impact of reaction temperature and H(2)O(2 )loading on the oxirane yield, under constant loading of acetic acid (5% wt.), using H2SO4 as catalyst (2% wt.). Experiments were monitored by quantifying oxirane oxygen content along reaction, and the assessed conditions were defined based upon a factorial design. Considering a two-phase reactive media, two kinetic models were proposed and the corresponding kinetic parameters were adjusted by regression of the experimental data. It was found that the model that included two oxirane ring opening reactions pathways better described the experimental results, and that it can be further used for process design and scale up. Finally, the validated model was used to optimize a batch UCOs epoxidation by mean of a multi-objective optimization approach. Results indicate that conversions below 88% are required to avoid oxirane ring opening reaction, obtaining a product with an oxirane oxygen content of 4.4% wt.

This article proposes a new formulation for the treatment of time-dependent constraints in the transient response optimization of structures. The novel method is based on constraint aggregation functions. However, instead of lumping the constraints in the physical domain, the method condenses the information of the time-dependent constraints into one equivalent function while retaining information about the point-wise constraints. The formulation is gradient compatible and allows a considerable reduction of the optimization problem. Two versions of the Kreisselmeier–Steinhauser function are studied. The formulation is tested on the size optimization of truss and framed three-dimensional structures subjected to dynamic loads. The methodology is tested in very-large transient response optimization problems in order to check its efficiency. Results show that the formulation is able guarantee the fulfilment of the constraints in the whole time interval studied. The size of the transient response optimization problem is highly reduced, allowing a reduction of the computational resources needed.

In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as a general formulation that includes some well-known meshfree methods as a particular case. The formulation is based on the use of Moving Least Squares (MLS) approximants as weight functions on a Galerkin formulation and to accurate discretize the convective and viscous fluxes. This formulation also verifies the discrete partition of unity and reproduces the zero-gradient condition for constant functions. Convective fluxes are discretized using Riemann solvers. In order to obtain high accuracy MLS is also used for the high-order reconstruction of the Riemann states. The accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems. (C) 2022 The Author(s). Published by Elsevier Inc.

In this work, a new discretization of the source term of the shallow water equations with non-flat bottom geometry is proposed to obtain a well-balanced scheme. A Smoothed Particle Hydrodynamics Arbitrary Lagrangian-Eulerian formulation based on Riemann solvers is presented to solve the SWE. Moving-Least Squares approximations are used to compute high-order reconstructions of the numerical fluxes and, stability is achieved using the a posteriori MOOD paradigm. Several benchmark 1D and 2D numerical problems are considered to test and validate the properties and behavior of the presented schemes.

A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.

Numerical simulation is nowadays a fundamental tool in science and engineering. It is involved in almost every discipline, and it is used in almost every field of research. In particular, computational fluid dynamics (CFD) has become an essential tool in both design and research. The development of numerical methods for the simulation of problems involving highly complex geometries, which are frequent in many engineering problems, remains a very active research field in computational fluid dynamics. However, current CFD methods suffer from a series of drawbacks: The use of CFD in the aerospace design process is severely limited by the inability to accurately and reliably predict turbulent flows with significant regions of separation and; nowadays, the standard numerical techniques in CFD are mainly grid-based methods. Mesh generation and adaptivity continue to be significant bottlenecks in the CFD workflow. In this context, the use of meshless methods may be interesting for problems involving deformable or moving boundaries in the propagation media or multiphase flows. Moreover, these methods do not require a mesh for the discretization, and then they can overcome one of the most important bottlenecks in the design process. In this work, we propose a new high-accurate, stable and low dissipative meshless method based on a Galerkin discretization of a set of conservation equations on an arbitrary Lagrangian Eulerian (ALE) approach, using moving least squares as weight functions for the Galerkin discretization. Differently to most common smooth particle hydrodynamics (SPH) approaches, the proposed method uses Riemann solvers instead of the artificial viscosity approach to prevent oscillations near shocks. The stability of the scheme is achieved by the recent a posteriori multi-dimensional optimal order detection paradigm. Using moving least squares (MLS) functions the partition of unity property is verified even near shocks, which allows the method to obtain very accurate results. Recent Publications 1. E Gaburov and K Nitadori (2011) Astrophysical weighted particle magnetohydrodynamics. Monthly Notices of the Royal Astronomical Society 414:129???154. 2. P F Hopkins (2015) A new class of accurate, mesh-free hydrodynamic simulation methods. Monthly Notices of the Royal Astronomical Society 450(1):53-110. 3. S Clain, S Diot and R Loubre (2011) A high-order finite volume method for systems of conservation laws - multidimensional optimal order detection (MOOD). Journal of Computational Physics 230:4028???4050. 4. X Nogueira, L Ramrez, S Clain, R Loubre, L Cueto Felgueroso and I Colominas (2016) High-accurate SPH method with multidimensional optimal order detection limiting. Computer Methods in Applied Mechanics and Engineering 310:134???155

In this work we present a delta-Smoothed Particle Hydrodynamics (SPH) scheme for weakly compressible flows with automatic adaptive numerical dissipation. The resulting scheme is a meshless self-adaptive method, in which the introduced artificial dissipation is designed to increase the dissipation in zones where the flow is under-resolved by the numerical scheme, and to decrease it where dissipation is not required. The accuracy and robustness of the proposed methodology is tested by solving several numerical examples. Using the proposed scheme, we are able to recover the theoretical decay of kinetic energy, even where the flow is under-resolved in very coarse particle discretizations. Moreover, compared with the original delta-SPH scheme, the proposed method reduces the number of problem-dependent parameters.