In this paper, a solution-adaptive algorithm is presented for the simulation of incompressible viscous flows. The framework of this method consists of an adaptive local stencil refinement algorithm and 3-points central difference discretization. The adaptive local stencil refinement is designed in such a manner that 5-points symmetric stencil is guaranteed at each interior node, so that convent...

In this work, the stencil adaptive method is applied to investigate the effects of a magnetic field on mixed convection of Al2O3-water nanofluid in a square lid-driven cavity. The incompressible Navier-Stokes equations are solved by an adaptive mesh method which has superior numerical advantages compared to the traditional method on the uniform fine grid. The main objective of this study is to ...

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

This paper presents a stencil adaptive phase-field lattice Boltzmann method (LBM) for the simulation of two-dimensional multiphase flows. In the phase-field model, the interface is viewed as a layer with finite thickness where physical parameters vary steeply and continuously. In the present study, a phasefield LBM is used. In this model, the Cahn–Hilliard equation can be correctly recovered by...

Multiresolution Time Domain (MRTD) techniques based on wavelet expansions can be used for adaptive refinement of computations to economize the resources in regions of space and time where the fields or circuit parameters or their derivatives are large. Hitherto, standard wavelets filter coefficients have been used with the MRTD method but the design of such filter itself may enable to incorpora...

The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

We present a class of energy-stable, high-order finite-difference interface closures for grids with step resolution changes. These grids are commonly used in adaptive mesh refinement of hyperbolic problems. The interface closures are such that the global accuracy of the numerical method is that of the interior stencil. The summation-by-parts property is built into the stencil construction and i...

Characterizing performance is essential to optimize programs and architectures. The open source Adaptive Sampling Kit (ASK) measures the performance trade-offs in large design spaces. Exhaustively sampling all points is computationally intractable. Therefore, ASK concentrates exploration in the most irregular regions of the design space through multiple adaptive sampling methods. The paper pres...

Characterizing performance is essential to optimize programs and architectures. The open source Adaptive Sampling Kit (ASK) measures the performance trade-off in large design spaces. Exhaustively sampling all sets of parameters is computationally intractable. Therefore, ASK concentrates exploration in the most irregular regions of the design space through multiple adaptive sampling strategies. ...

Similar in nature to an image mosaic, a photo-stencil is a rendering of a binary target image by an arrangement of smaller binary stencil images. This paper presents a method for efficiently creating photo-stencil images, making use of the Fast Fourier Transform to speed up costly computations. The resulting photo-stencils are a new and interesting form of nonphotorealistic rendering.