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• A two-step monolithic method for the efficient simulation of incompressible flows

  P. Ryzhakov, J. Cotela, R. Rossi, E. Oñate

  Int. J. Numer. Meth. Fluids (2014). Vol 74 (12), pp. 919-934

  
  

  Abstract

  We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists in solving the discrete nonlinear system of governing equations in two steps: introducing ‘artificial’ compressibility first and afterwards correcting the solution by solving the original incompressible system. The speed‐up is obtained because of a better conditioning of the modified discrete system solved at the prediction step. The formulation can be easily implemented into existing monolithic codes requiring minor modification only. The paper concludes with two examples validating the formulation and facilitating the estimation of the obtained speed‐up. For the tests chosen, an average speed‐up is approximately double, suggesting that the method is a feasible approach for incompressible flows' simulation. 

  Abstract
  We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists [...]

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• Multi-objective aerodynamic shape optimization using MOGA coupled to advanced adaptive mesh refinement

  M. Kouhi, D. Lee, G. Bugeda, E. Oñate

  Computers and Fluids (2013). Vol. 88, pp. 298-312

  
  

  Abstract

  This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off between the mesh refinement during the optimization process and the improvement of the optimized solution. This subject is investigated in the transonic airfoil design optimization using an Adaptive Mesh Refinement (AMR) technique coupled to Multi-Objective Genetic Algorithm (MOGA) and an Euler aerodynamic analysis tool. The methodology is implemented to solve three practical design problems; the first test case considers a reconstruction design optimization that minimizes the pressure error between a predefined pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coefficient (Cl). The solutions obtained with and without adaptive mesh refinement are compared in terms of solution improvement and computational cost. Numerical results clearly show that the use of adaptive mesh refinement can improve the solution accuracy while reducing significant computational cost in both single- and multi-objective design optimizations.

  Abstract
  This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off [...]

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• An efficient edge‐based level set finite element method for free surface flow problems

  R. Rossi, E. Oñate, A. LARESE, P. Dadvand

  Int. J. Numer. Meth. Fluids (2013). Vol. 71 (6), pp. 687-716

  
  

  Abstract

  We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution scheme is proposed. A custom data structure, obtained by blending node‐based and edge‐based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples

  Abstract
  We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit [...]

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• Robust active shock control bump design optimisation using hybrid parallel MOGA

  D. Lee, G. Bugeda, J. Périaux, E. Oñate

  Computers and Fluids (2013). Vol. 80, pp. 214 - 224

  
  

  Abstract

  The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFDs) software. For MOEA, Robust Multi-Objective Optimisation Platform (RMOP) developed at CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto-Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. Numerical results show not only how the concept of Shock Control Bump (SCB) coupled to CFD can improve aerodynamic performance of classic transonic aerofoil at the variability of flight conditions but also how high performance (parallel/distributed) computation with applying Hybrid-Game increases the efficiency of optimisation in terms of computational cost and results accuracy

  Abstract
  The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary [...]

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• An algorithm for the simulation of thermally coupled low speed flow problems

  P. Ryzhakov, E. Oñate, R. Rossi

  Int. J. Numer. Meth. Fluids (2012). Vol. 70' (1), pp. 1-19

  
  

  Abstract

  In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes equations, written in nonconservation form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum-continuity system. If an explicit single-step time integration scheme for the energy equation is used, the decoupling results to be natural. Integration of the momentum-continuity system is carried out using a semi-explicit method, combining Runge–Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma ≪ 1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution. The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum-continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge–Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme. The method is tested using two benchmark examples.

  Abstract
  In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes [...]

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• Hybrid-Game Strategies for multi-objective design optimization in engineering

  D. Lee, L. González, J. Periaux, A. Srinivas, E. Oñate

  Computers and Fluids (2011). Vol. 47 (1), pp. 189-204

  
  

  Abstract

  A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated

  Abstract
  A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their [...]

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• Lift maximization with uncertainties for the optimization of high‐lift devices

  Z. Tang, J. Périaux, G. Bugeda, E. Oñate

  Int. J. Numer. Meth. Fluids (2010). Vol. 64 (2), pp. 119-135

  
  

  Abstract

  In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the modified non‐dominated sorting genetic algorithms are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier–Stokes computation using an unstructured mesh. In order to reduce the number of expensive evaluations of the fitness function a response surface modeling is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem, a semi‐torsional spring analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high‐lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free‐stream angle of attack at landing flight condition.

  Abstract
  In this paper, the aerodynamic shape optimization problems with uncertain operating conditions have been addressed. After a review of robust control theory and the possible [...]

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• Simulation of flows with violent free surface motion and moving objects using unstructured grids

  R. Löhner, C. Yang, E. Oñate

  Int. J. Numer. Meth. Fluids (2007). Vol. 53 (8), pp 1315-1338

  
  

  Abstract

  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three‐dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam‐break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.

  Abstract
  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]

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• Optimum aerodynamic shape design including mesh adaptivity

  G. Bugeda, E. Oñate

  Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 915-934

  
  

  Abstract

  This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. This sensitivity analysis is described for the incompressible potential equations and the Euler equations. The efficiency of the proposed method is checked by means of two 2D inverse problems.

  Abstract
  This paper presents a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation [...]

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• A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems

  E. Oñate, M. Manzán

  Int. J. Numer. Meth. Fluids (1999). Vol. 31 (1), pp. 203-221

  
  

  Abstract

  A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance equation for the transient case derived by Oñate [Comput. Methods Appl. Mech. Eng., 151, 233–267 (1998)] using a finite increment calculus approach. A description of the new stabilization method and a procedure for computing the stabilization parameter of the space–time solution is given. The efficiency of the stabilization approach is shown in the solution of some transient advective–diffusive problems, including the non‐linear Burger's equation. 

  Abstract
  A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance [...]

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