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This paper presents an adaptive Discontinuous-Galerkin finite element method to solve linear advection–reaction equations. The method was developed for the prediction of hemolysis in prosthetic devices, where the flow may include recirculation zones. To ensure the well-posedness of the problem, we solve the transient form of the PDE. Time discretization is achieved with an implicit Euler scheme in order to obtain the steady-state solution rapidly. Linear interpolation functions are used to approximate the hemolysis field. The a posteriori estimation of the error is obtained by solving an advection–reaction equation for the error, which is approximated with quadratic interpolation functions. Then, elementary estimations of the error are computed using a semi-norm developed to achieve the best possible results, even in the presence of recirculation. Code verification – to assess the convergence and conservation properties of the method – is performed with the method of manufactured solutions and with a conservation test using a sharp gaussian function as a reaction term. Excellent results are obtained in both cases. Predictions of hemolysis in a dialysis cannula are presented as an engineering application of our method. [Copyright &y& Elsevier]

Three issues related to good computational fluid dynamics (CFD) practice are discussed. First, adaptive methods are shown to be a simple tool to perform systematic grid refinement studies needed to achieve solutions with controlled accuracy (verification of simulations). Second, it is shown that the sensitivity equation method prorides insights about which parameters critically affect the flow response. Finally, flow sensitivities are used to propagate model parameter uncertainties through the CFD code to yield uncertainty estimates of the CFD predictions. This provides a rigorous framework for comparing predictions to measurements (validation of predictions). These combined approaches help to build confidence in CFD predictions and develop good CFD practice. The resulting uncertainty bars put CFD on par with experimental techniques. The approaches are demonstrated on two-dimensional problems: a k-∈ model of the flow in an annular turn-around duct and conjugate free convection with variable fluid properties. Taken together, these approaches offer a good prospect for developing families of computing methods that can be viewed as standards of good practice in CFD, ensuring that verification and validation studies are performed on solid grounds. [ABSTRACT FROM AUTHOR]