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The goal of this work is to present a new methodology to solve computationalfluid dynamics (CFD) problems based on a particle method minimizing the usage of meshbased solvers in order to get a potential computational efficiency to get rid of the newchallenges of engineering and science. Thanks to the recent advances in hardware, inparticular the possibility of using graphic processors (GPGPU), high performance computingis now available if and only if software development gives an important jump to incorporatethis technology. Due to the complexity in programming over such a platform the best way totake advantage of its performance rests on the design of numerical methods able to be viewedas cellular automata. In this sense explicit methods seem to be an attractive choice. However itis well known that explicit methods have a severe stability limitation. On the other hand, thespatial discretization of particle methods offers some advantages against others like finiteelements or finite volumes in terms of computational costs. The main reasons of this rest onthe low dimensionality of this method (particle methods are a zero dimensional representationof the solution of a given set of PDEs while finite elements are 3D and finite volume are part2D and part 3D). In addition particle methods are generally written in Lagrangian formulationavoiding the necessity of defining a spatial stabilization in convection dominated flows. Finiteelements and finite volume are generally designed using an Eulerian formulation with someextra diffusion in the solution due to this stabilization requirement. However, some particlemethods often require a mesh to interpolate and also to solve the problem losing some of theiradvantages in terms of efficiency. Even though there are some methods that do not use anymesh in their formulation, the interpolation methods become very complex introducing errorsin the computation with noticeable extra diffusion. Having detected two main limitations of particle methods to solve Navier-Stokes equations for viscous incompressible flows, wepropose in this work the following: to enhance the time integration using an explicitstreamline based scheme computed with the old velocity vector allowing to enlarge the timesteps of standard explicit schemes in advection dominated flows in order to minimize the useof mesh based solvers, the velocity predictor and its correction is formulated purely on theparticles as any spatial collocation method using a gradient recovery technique to include thepressure gradient and the viscous terms. This method is written in a Lagrangian formulation ina segregated way like a fractional step method. The computation of the predicted fractionalvelocity and its correction is done using our proposal explained above, i.e. streamline in timecollocation in space scheme. On the other hand the pressure correction (Poisson solver) iscarried out using a FEM like method. This method may be implemented in two ways: themobile mesh version: where the particles represent the mesh nodes and a permanentremeshing is needed in order to avoid the severe restriction in the time steps imposed by themesh motion. Remember that the mesh is only used to solve the Poisson problem for thepressure correction. the fixed mesh version: where there is a background mesh to do somecomputations, mainly for the pressure, and a certain amount of particles that move in aLagrangian way transporting the velocity. Some interpolation between the particles and thefixed mesh is needed but the remeshing is completely avoided. This paper presents this novelapproach built with the above mentioned features and shows some results to demonstrate itsability in terms of stability and accuracy with a high potential to be optimized in order to solvethe challenging engineering problems of the next decades.

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