A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds

In this article we introduce a FCT stabilized Radial Basis Function (RBF)-Finite Difference (FD) method for the numerical solution of convection dominated problems. The proposed algorithm is designed to maintain mass conservation and to guarantee positivity of the solution for an almost random placement of scattered data nodes. The method can be applicable both for problems defined in a domain or if equipped with level set techniques, on a stationary manifold. We demonstrate the numerical behavior of the method by performing numerical tests for the solid-body rotation benchmark in a unit square and for a transport problem along a curve implicitly prescribed by a level set function. Extension of the proposed method to higher dimensions is straightforward and easily realizable

Numerical study of the RBF-FD level set based method for partial differential equations on evolving-in-time surfaces

In this article we present a Radial Basis Function (RBF)-Finite Difference (FD) level set based method for numerical solution of partial differential equations (PDEs) of the reaction-diffusion-convection type on an evolving-in-time hypersurface Γ (t). In a series of numerical experiments we study the accuracy and robustness of the proposed scheme and demonstrate that the method is applicable to practical models

MESHLESS METHODS FOR SOLVING REACTION-DIFFUSION PROBLEMS-A BRIEF REVIEW

Reaction-diffusion equations represent many important and critical applications in engineering and science. Numerical techniques play an important role for solving such equations accurately and efficiently. This paper presents a brief review of meshless methods for solving general diffusion equations, including reaction-diffusion systems

Effect logs of double diffusion on MHD Prandtl nano fluid adjacent to stretching surface by way of numerical approach

AbstractThe current communication is carried to contemplate the unique and novel characteristics of nanofluids by constructing formulation of Prandtl fluid model. The fascinating aspects of thermo diffusion effects are also accounted in this communication. Mathematical modelling is performed by employing boundary layer approach. Afterwards, similarity variables are selected to convert dimensional non-linear system into dimensionless expressions. The solution of governing dimensionless problem is executed by shooting method (SM). Graphical evaluation is displayed to depict the intrinsic behavior of embedded parameters on dimensionless velocity, temperature, solutal concentration and nanoparticle concentration profiles. Furthermore, the numerical variation for skin friction coefficient, local Nusselt number, Sherwood number and nano Sherwood number is scrutinized through tables. The assurance of current analysis is affirmed by developing comparison with previous findings available in literature, which sets a benchmark for implementation of computational approach. It is inferred from the computation that concentration profile increases whereas Sherwood number decreases for progressive values of Dufour solutal number

Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications

The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve fine-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their efficiency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of filtration, insulating materials, and turbulence

Numerical Simulations

This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation