Tiago Quintino

The COOLFluiD framework: design solutions for high performance object oriented scientific computing software

The numerical simulation of complex physical phenomena is a challenging endeavor. Software packages developed for such purpose should combine high performance and extreme flexibility, in order to allow an easy integration of new algorithms, models and functionalities, without penalizing run-time efficiency. COOLFluiD is an object-oriented framework for multi-physics simulations using multiple numerical methods on unstructured grids, aiming at satisfying these needs. To this end, specific design patterns and advanced techniques, combining static and dynamic polymorphism, have been employed to attain modularity and efficiency. Some of the main design and implementation solutions adopted in COOLFluiD are presented in this paper, in particular the Perspective and the Method-Command Patterns, used to implement respectively the physical models and the numerical modules.

Reusable object-oriented solutions for numerical simulation of PDEs in a high performance environment

Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods) that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.

Third order residual distribution schemes for the Navier-Stokes equations

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P2 Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.

Conservative Multidimensional Upwind Residual Distribution Schemes for Arbitrary Finite Elements

We introduce monotone first order fluctuation splitting schemes for solving hyperbolic systems on arbitrary finite elements, thereby generalizing the N-scheme previously proposed for linear P1 triangles. Conservation is retained by relaxing on strict monotonicity, using a simple method based on contour integration over the element boundaries. Numerical examples are given for the Euler equations solved on Q1 elements for applications ranging from transonic to hypersonic regimes.

High-order upwind residual distribution schemes on isoparametric curved elements

Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic and cubic approximation of the boundaries of the domain, using standard sub- or isoparametric transformation. Numerical results for the Euler equations confirm the predicted order of accuracy, showing the importance of a higher order approximation of the geometry.

The COOLFluiD parallel architecture

This paper discusses the parallel design of COOLFluiD (Computa- tional Object Oriented Library for Fluid Dynamics), a state-of-the-art C++ framework for multi-physics simulations using multiple numerical methods on unstructured grids. By using advanced techniques and specific design patterns, flexibility and modularity are assured. COOLFluiD was recently adapted to support parallel computations on distributed memory machines. For this, a parallel layer was added, designed to minimize impact on both users and software developers, while maintaining high performance. From the user’s point of view, parallelisation is fully transparent. The techniques making this possible will be discussed. Also presented is a technique for reconciling generic programming with libraries requiring explicit type information.

Application of Residual Distribution Method for Acoustic Wave Propagation

This article deals with the discretization of Linearized Euler Equations (LEEs) by multidimensional upwind Residual Distribution methods. Linearized Euler equations are applied in the domain where there is no source of sound and the analogy methods such as Ffowcs-Williams can not be used because of gradients in the mean flow. Residual distribution method is a class of schemes that is in between finite-element and finite-volume. In particular, the schemes that we use are multidimensional upwind which make them very attractive because of their very low cross-dissipation. First, we define the formulation of the LEEs that we choose to use. Then, we focus on the residual schemes and we describe two ways of discretizing unsteady problems. The third part presents a wave number of those schemes. Finally, we show the advantage of these schemes on several acoustic problems.

Run-time automatic instantiation of algorithms using C++ templates

Algorithms for scientific computations implemented with template C++ code are both generic and highly efficient. Nevertheless, once compiled, they become statically bound to some functionality. To allow the end-user to change functionality and configure the algorithms with external policies they must retain their generality at run-time. For this purpose, we introduce a technique that uses delayed run-time instantiation of C++ template algorithms. It generates code from a predefined collection of algorithms, configured with policy classes chosen at run-time. The code is then compiled into a dynamically library that is loaded on demand by the end-user into the scientific simulation tool.

Unsteady High Order Residual Distribution Schemes with Applications to Linearised Euler Equations

This article is dedicated to the design of high order residual distributive schemes for unsteady problems. We use a space-time strategy, which means that the time is considered as a third dimension. To achieve high order both in space and in time, we use prismatic elements having (k+1) levels, each level being a P k element. The first section is dedicated to the deign of space-time schemes on such elements. The second section presents the performances on different type of problems. In particular, we look at a discontinuous problem on Euler equations and two problems of propagation of sound using Linearised Euler equations.

High Order Residual Distribution Schemes Based on Multidimensional Upwinding

We present an extension of the multidimensional upwind distributive schemes to high order solution spaces. We look into different high-order discretization issues such as: quadratic and cubic boundary curvature; monotonicity of the schemes in presence of solutions with discontinuities; discretisation of temporal terms for unsteady applications and discretization of diffusive fluxes. Results of test cases representative of all these issues are presented.