Search Results

• Linear stability of a non-Newtonian hydromagnetic Casson fluid in a channel flow is studied.

We study the temporal stability of linear two-dimensional disturbances of plane Poiseuille flow of a Casson fluid in a rigid parallel channel under the influence of a uniform magnetic field. When the disturbance is taken in normal mode ...

We propose a new algorithm to improve the accuracy of spectral methods for singularly perturbed two-point boundary value problems. Driscoll and Hale [J. Numer. Anal., 36 (2016), pp. 108--132] suggest resampling as an alternative to row replacement when ...

A smoothness-increasing accuracy conserving filtering approach to the regularization of discontinuities is presented for single domain spectral collocation approximations of hyperbolic conservation laws. The filter is based on convolution of a ...

We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these ...

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of ...

A new explicit expression of the higher order pseudospectral differentiation matrices is presented by using an explicit formula for higher derivatives of Chebyshev polynomials. The roundoff errors incurred during computing differentiation matrices are ...

We present a method for the numerical solution of partial differential equations using spectral collocation. By employing a structured representation of linear operators we are able to use fast algorithms without being restricted to periodic boundary ...

In this paper, an analytical approximate solution of Euler equations is obtained by a collocation method. The collocation method uses two variables Chebyshev polynomial basis and collocation coefficients are obtained solving polynomial equations by ...

A Chebyshev collocation method is applied to the study of a thermal convection problem in the primitive variable formulation. This method has been succesfully applied to cylindrical coordinates and now it is extended to cartesian coordinates. The main ...

A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the ...

While the Chebyshev pseudospectral method provides a spectrally accurate method, integration of partial differential equations with spatial derivatives of order M requires time steps of approximately $O(N^{-2M})$ for stable explicit solvers. Theoretically,...

We present in this paper numerical simulations of reactive flows interacting with shock waves. We argue that spectral methods are suitable for these problems and review the recent developments in spectral methods that have made them a powerful numerical ...

As a continuation of the efficient and accurate polynomial interpolation time-marching technique in one-dimensional and two-dimensional cases, this paper proposes a method to extend it to three-dimensional problems. By stacking all two-dimensional (x, y)...

A new method is investigated to reduce the roundoff error in computing derivatives using Chebyshev collocation methods. By using a grid mapping derived by Kosloff and Tal-Ezer, and the proper choice of the parameter $\alpha$, the roundoff error of the kth ...

We study several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed ...

A mixed problem and its approximation in an abstract framework are considered. They are proved to be well posed if and only if several inf-sup conditions are satisfied. These results are applied to the Stokes equations in a square, formulated in Chebyshev ...