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Showing 1 to 15 of 15 for “"spectral collocation"”.
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Spectral collocation method for compact integral operators
<p>We propose and analyze a spectral collocation method for integral</p> <p>equations with compact kernels, e.g. piecewise smooth kernels and</p> <p>weakly singular kernels of the form $\frac{1}{|t-s|^\mu}, \;</p> <p>0<\mu<1. $ We prove that 1) for integral equations, the convergence</p> <p>rate …
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Discontinuous Galerkin solutions of the Boltzmann equation: spectral collocation and moment methods
… are presented and compared. The first uses a spectral collocation basis in velocity space. The resulting system is solved in time using Diagonally Implicit Runge-Kutta methods, chosen in order to mitigate stiffness concerns. A Jacobian-Free Newton—Krylov method is presented, accelerated with a …
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The Computation of Exact Green's Functions in Acoustic Analogy By a Spectral Collocation Boundary Element Method
… The exact Green's function is computed using a spectral collocation boundary element method that can easily accommodate complex geometries. A frequency-domain spectral collocation method is applied to both smooth and non-smooth boundaries, resulting in exponential convergence on smooth …
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High-Order Positivity-Preserving <i>L<sub>2</sub></i>-Stable Spectral Collocation Schemes for the 3-D Compressible Navier-Stokes Equations
… class of positivity-preserving, entropy stable spectral collocation schemes for the 3-D compressible Navier-Stokes equations. The key distinctive property of our method is that it is proven to guarantee the pointwise positivity of density and temperature for compressible viscous flows. The new …
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Spectral Methods For The Hamiltonian Systems
<p>We conduct a systematic comparison of spectral methods with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> …
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Wave interactions in three-dimensional boundary layers
… using the method of multiple scales and a spectral collocation numerical method. Detuning parameters for the wavenumbers and frequencies and the effects of the growth of the boundary layer are included in the modeling. The spatial and temporal growth of numerous triads consisting of …
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Study of flow past elliptic and circular cylinders using direct numerical simulation
… body wakes. With this in mind, a single-domain, spectral collocation technique has been developed to simulate the full three-dimensional incompressible flow over elliptic cylinders. Results of two- and three-dimensional simulations for a range of flow and geometric parameters are presented. The …
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Linear stability analysis of non-reacting and reacting elliptical jets
… formulated by applying the Chebyshev and Fourier spectral collocation method to the disturbance equations of the flow expressed in a generalized cylindrical coordinate system. The resulting algebraic eigenvalue problem was solved using the inverse power method. The approach developed is capable of …
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Numerical methods for fractional differential equations by new caputo and hadamard types operators
… method, finite difference scheme and spectral collocation method in this research for FODE and FPDE. Caputo-Fabrizo operator is a definition which is verified that does not fit the usual concept neither for fractional nor for integer derivative integral. The main interest of this …
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Elongational Flows in Polymer Processing
… of the spectrum of its generator. By using a spectral collocation method, we shall derive numerical results on the eigenvalue distribution, thereby confirming prior results on the stability of the steady-state solution.
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Implicit-explicit methods for time-dependent PDE’s
… have been used, especially in conjunction with spectral methods. For convection-diffusion problems, for example, one would use an explicit scheme for the convection term and an implicit scheme for thediffusion term. Reaction-diffusion problems can also be approximated in this manner. In this …
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Direct Numerical Simulation of Flow Over Circular Cylinders for Large -Eddy Simulation Modeling
… computational method uses a Fourier-Chebyshev spectral collocation for the spatial discretization, and boundary conditions that account for the displacement effect of the cylindrical body. The results of the simulation are analyzed and we find good comparison with mean and root-mean-square …
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Modelling of liquid droplet dynamics in a high DC magnetic field
… model is a grid point formulation of the pseudo-spectral collocation method discretised in a spherical coordinate system with the implicit Euler method used to advance the solution in time. A coordinate transformation method is used to ensure the direct surface tracking required for modelling the …
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Studies on secondary instabilities
… eigenvalue problem through the application of a spectral collocation method Following Floquet theory, previous analysis looked for subharmonic (wavelength 2 λ) and fundamental (wavelength λ) types of solutions. We extend the Floquet theory to solutions having arbitrary wavelengths, hence …
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High accuracy computational methods for the semiclassical Schrödinger equation
The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised …