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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. • Neural network to compute the weighting functions for WENO5 schemes. • The proposed scheme generalizes for different grid resolutions and problems. • The neural-network based scheme outperforms several WENO5 schemes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, a new method for structural topology optimization considering minimum weight and local stress constraints is proposed. For this purpose, the Overweight Approach, an improvement of the so-called Damage Approach, is used. In this method, a virtual relative density is defined as a function of the violation of the local stress constraints. The virtual relative density is increased as stresses exceed the maximum allowable value. The optimization algorithm will provide a design with a minimal variation of the relative density. The structural analysis is performed by means of the Finite Element Method (FEM) and the distribution of material is modelled in terms of a uniform relative density within each element. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP). Finally, the proposed methodology is tested by means of some benchmark problems, and the results show that the Overweight Approach is a feasible alternative for the Damage Approach and the stress constraint aggregation techniques. • An alternative damage approach to solve the topology optimization problem is developed. • A uniform relative density per element is considered to define the material layout. • Intermediate densities are penalized to attain solutions easily manufacturable. • Several benchmark examples in the topology optimization field are solved. • Solutions with high spatial definition can be obtained in a reduced CPU time. [ABSTRACT FROM AUTHOR]

• A high-accurate meshless method for compressible viscous flows is presented. • MLS is used instead of kernel functions to satisfy the partition of unity property. • New reconstruction of Riemann states based on MLS instead of Taylor polynomials. • A set of numerical examples for several flow regimes are analyzed. 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. [ABSTRACT FROM AUTHOR]