Revisting High-Resolution Schemes with van Albada Slope Limiter

Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.

Transparent Object Reconstruction Based on Compressive Sensing and Super-Resolution Convolutional Neural Network

The detection and reconstruction of transparent objects have remained challenging due to the absence of their features and variations in the local features with variations in illumination.In this paper,both compressive sensing(CS)and super-resolution convolutional neural network(SRCNN)techniques are combined to capture transparent objects.With the proposed method,the transparent object’s details are extracted accurately using a single pixel detector during the surface reconstruction.The resultant images obtained from the experimental setup are low in quality due to speckles and deformations on the object.However,the implemented SRCNN algorithm has obviated the mentioned drawbacks and reconstructed images visually plausibly.The developed algorithm locates the deformities in the resultant images and improves the image quality.Additionally,the inclusion of compressive sensing minimizes the measurements required for reconstruction,thereby reducing image post-processing and hardware requirements during network training.The result obtained indicates that the visual quality of the reconstructed images has increased from a structural similarity index(SSIM)value of 0.2 to 0.53.In this work,we demonstrate the efficiency of the proposed method in imaging and reconstructing transparent objects with the application of a compressive single pixel imaging technique and improving the image quality to a satisfactory level using the SRCNN algorithm.

A TV-Based Iterative Regularization Method for the Solutions of Thermal Convection Problems

Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable(PV)solutions corrupted by uniformly distributed randomnoises are numerically studied through the natural convection(NC)aswell as the mixed convection(MC)environment.The most recognizable filter-scheme is based on a combination of the negative Laplace equation multiplied with the selection of the spatial scale and a linear function in order to preserve the uniqueness of the filtered solution.A more complicated filter-scheme,based on a Stokes problem which couples a filtered velocity and a filtered(artificial)pressure(or Lagrange multiplier)in order to enforce the incompressibility constraint,is also studied.Linear and Stokes basedfilters via nested iterative(NI)filters and the consistent splitting scheme(CSS)are proposed for the NC/MC problems.Inspired by the total-variation(TV)model of image diffusion,well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS.Our experimental results show that our proposed algorithms are effective and efficient in eliminating the unwanted spurious oscillations and preserving the accuracy of thermal convective fluid flows.