Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the influence of both thermal and solutal stratification on magneto-hydrodynamics (MHD) nanofluid flow along an exponentially stretching sheet is examined.
Abstract: The present analysis concentrates to examine the influence of both thermal and solutal stratification on magneto-hydrodynamics (MHD) nanofluid flow along an exponentially stretching sheet. Moreover, simultaneous effects of mixed convection and viscous dissipation are also analyzed to determine the thermal conductivity within the restricted domain. Energy and concentration equation consist of two important slip mechanisms, namely: the Brownian motion of nanoparticles and the thermophoresis due to concentration difference. By the mean of compatible similarity transformed, a system of PDEs is converted into the system of nonlinear ODEs. The resulting nonlinear ODEs are successfully solved via the implicit finite difference method (FDM). Obtained numerical solutions are plotted for each profile for different and converging values of including parameters. To validate the results, numerical values of Nusselt number are compared with the existing literature for a particular case. Obtained results present the significant impact of each parameter on temperature and concentration. Nanofluid flow behaviour is also observed via velocity profile.
91 citations
TL;DR: In this article, a new method for solving multidimensional inverse heat conduction problems using control volume methods is presented, where the partial heat-conduction equation is replaced by a system of ordinary differential equations in time, which are then solved sequentially.
90 citations
TL;DR: Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidean error minimization are investigated and numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported on.
Abstract: We consider conjugate gradient type methods for the solution of large linear systemsA x=b with complex coefficient matrices of the typeA=T+i?I whereT is Hermitian and ? a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidean error minimization, respectively, are investigated. In particular, we propose numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices and derive error bounds for all three methods. It is shown how the special shift structure ofA can be preserved by using polynomial preconditioning, and results on the optimal choice of the polynomial preconditioner are given. Also, we report on some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation.
90 citations
TL;DR: In this paper, the surface impedance boundary conditions (SIBC) for the finite-difference time-domain (FDTD) method is presented, in which the impedance function of a lossy medium is approximated with a series of first-order rational functions.
Abstract: An efficient way to implement the surface impedance boundary conditions (SIBC) for the finite-difference time-domain (FDTD) method is presented in this paper. Surface impedance boundary conditions are first formulated for a lossy dielectric half-space in the frequency domain. The impedance function of a lossy medium is approximated with a series of first-order rational functions. Then, the resulting time-domain convolution integrals are computed using recursive formulas which are obtained by assuming that the fields are piecewise linear in time. Thus, the recursive formulas derived here are second-order accurate. Unlike a previously published method [7] which requires preprocessing to compute the exponential approximation prior to the FDTD simulation, the preprocessing time is eliminated by performing a rational approximation on the normalized frequency-domain impedance. This approximation is independent of material properties, and the results are tabulated for reference. The implementation of the SIBC for a PEC-backed lossy dielectric shell is also introduced. >
90 citations
TL;DR: The GFD explicit formulae developed to obtain the different derivatives of the pde's are based on the existence of a positive definite matrix that it is obtained using moving least squares approximation and Taylor series development.
90 citations