In this study, we report development of two innovatory parallel implementations of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). MPDATA is the main module of the multiscale fluid model EULAG [Prusa et al., Computers & Fluids, vol. 37, 2008]. Recently, the dynamical core of EULAG has been implemented into COSMO (Consortium for Small-scale Modeling) weather prediction framework and is expected to be in operational use. The original code of MPDATA is written in

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... RAN77 and has excellent efficiency and scalability on conventional supercomputer architectures. The new C++ implementations are designed and optimized under modern CPU and GPU based high-performance computing platforms. A number of innovatory solutions have been employed in these codes, including stencil decomposition, block decomposition (with weighting analysis between computation and communication), reduction of intercache communication by partitioning of cores into independent teams, cache reusing and vectorization. The new techniques allow to take the full advantage of the new architectures and accelerate the code execution. The correctness and accuracy of the new implementations are examined based on a standard three-dimensional solid body rotation test case. Additionally, we focus on testing computational efficiency and scalability. In most runs and especially in simulations with larger computational grids the new codes performed better than the traditional implementation. Index Terms-MPDATA, advection solver, parallel computing.