Keywords: POD reduced order model 3D flows Finite element Unstructured mesh Numerical simulation a b s t r a c t A new scheme for implementing a reduced order model for complex mesh-based numerical models (e.g. finite element unstructured mesh models), is presented. The matrix and source term vector of the full model are projected onto the reduced bases. The proper orthogonal decomposition (POD...

A three-dimensional semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic anelastic equations, suitable for simulation of small-to-mesoscale atmospheric flows. The model builds on nonoscillatory forwardin-time MPDATA approach using finite-volume discretization and admitting unstructured meshes with arbitrarily shaped cells. The numerical advancements are e...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...

3D Hybrid Finite Element Finite Difference Time Domain (FE/FDTD) Method is developed and applied to the numerical modeling of antennas. The antenna geometry is modeled using tetrahedral finite element mesh. Pyramidal elements are introduced in the transition from unstructured tetrahedral elements to structured hexahedral elements. The finite element formulation incorporates the excitation of an...

This chapter describes the general principles of unstructured mesh generation in two and three dimensions, together with the use of finite elements in modelling space plasmas. Particular attention is given to the requirement of generating meshes that are aligned along magnetic field lines, in order to properly capture the strong anisotropy of magnetised plasmas. Example results are given in 2D ...

Stochastic chemical systems with diffusion are modeled with a reactiondiffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reactiondiffusion master equation. The space...

This work is related with the implementation of a finite volume method to solve the 2D Shallow Water Equations on Graphic Processing Units (GPU). The strategy is fully oriented to work efficiently with unstructured meshes which are widely used in many fields of Engineering. Due to the design of the GPU cards, structured meshes are better suited to work with than unstructured meshes. In order to...

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ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For u...