Abstract: In this paper, we formulate the permeability inverse problem in the Bayesian framework using total variation (TV) and $\ell_p$ regularization prior. We use the Markov Chain Monte Carlo (MCMC) method for sampling the posterior distribution to solve the ill-posed inverse problem. We present simulations to estimate the distribution for each pixel for the image reconstruction of the absolute permeability.

Abstract: This paper proposes a new enhanced velocity method to directly construct a flux-continuous velocity approximation with multipoint flux mixed finite element method on subdomains. This gives an efficient way to perform simulations on multiblock domains with non-matching hexahedral grids. We develop a reasonable assumption on geometry, discuss implementation issues, and give several numerical results with slightly compressible single phase flow.

Abstract: In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectored thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., Matlab and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectored operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

Abstract: In the development of a numerical model for aeroacoustic problems, two main issues arise: which level of physical approximation to adopt and which numerical scheme is the most appropriate. It is possible to consider a hierarchy of physical aproximations, ranging from the wave equation, without or with convective effects, to the linearized Euler and Navier-Stokes equations, as well as a wide range of high-order numerical schemes, ranging from compact finite difference schemes to the discontinuous Galerkin method (DGM) for unstructured grids. For problems in complex geometries, significant hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes, may occur. For example in ducts with sudden changes of area where flow separation occurs in correspondence of sharp edges with a consequent generation of vorticity for viscous effects. To correctly model this coupling, the Navier-Stokes equations, linearized with respect to a representative mean flow, must be solved. The formulation based on Linearized Navier-Stokes (LNS) equations is suitable to deal with problems involving such hydrodynamic-acoustic interactions. The occurrence of geometrical complexities, such as sharp edges, where acoustic energy is transferred into the vortical modes for viscous effects, requires an highly accurate numerical scheme with non only reduced dispersive properties, to accurate model the wave propagation, but also providing a very low level of numerical dissipation on unstructured grids. The DGM is the most appropriate numerical scheme satisfying these requirements. The objective of the present work is to develop an efficient numerical solution of the LNS equations, based on a DGM on unstructured grids. To our knowledge, there is only one work dealing with the solution of the LNS for aeroacoustics where the equations are solved in the frequency domain. In this work we develop the method in the time domain. The non-dispersive and non-diffusive nature of acoustic waves propagating over long distances forces us to adopt highly accurate numerical methods. DGM is one of the most promising scheme due to its intrinsic stability and to its capability to treat unstructured grids. Both advantages make this method well suited for problems characterized by wave propagation phenomena in complex geometries. The main disadvantage of DGM is the high computational requirements because the discontinuous character of the method which adds extra nodes on the interfaces between cells respect to a standard continuous Galerkin Method (GM). Techniques of optimization of the DGM in the case of the Navier-Stokes equations, to reduce the computational effort, are currently object of intense research. At our knowledge, no similar effort is made in the context of the solution of the LNS equations. The LNS equations are derived and the DGM is presented. Preliminary results for the case of the scattering of plane waves traveling in a duct with a sudden area expansion and a comparison between LEE and LNS calculations of vortical modes, are presented.