Higher-order implicit-explicit multi-domain compressible Navier-Stokes solvers

Abstract

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Fast FC-based Implicit Navier Stokes solver. • Spectral algorithm for the Navier-Stokes equations in general domains. • Multi-domain parallel algorithm. • Implicit-explicit implementations exhibiting. • high-order convergence in space and time.

Fourier continuation method for incompressible fluids with boundaries

“…Using Eqs. (54) and (55) we can construct a random and incompressible 3D vector by generating a superposition of the q functions with random phases and amplitudes for both the a nlm and b nlm coefficients in the range 4 ≤ k 2…”

Skin effect in neutron transport theory

“…where u n+1 j ∼ u(v, ξ j , t n+1 ), t n+1 = n t, and where α k and β are the coefficients for the third-order BDF formula. (The FC method enables representation of general smooth nonperiodic functions by a Fourier series while avoiding the well-known Gibbs ringing phenomenon, with applicability to the solution of partial differential equations in general multidimensional spatial domains with high accuracy and negligible numerical dispersion [31][32][33].) Figure 4 demonstrates the excellent convergence properties of the algorithm, for μ s = μ a = q = 1.…”

“…[30]], to avoid the inversion of large matrices at each time step. Using the identity operator 1 and the Fourier continuation (FC) spectral differentiation operator D [31][32][33], the resulting discrete version of Eq. ( 8), which amounts to an implicit version of the FC discrete ordinates (FC-DOM) method [33], thus reads…”

Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions

“…Another advantage of the FC-Gram method is that Poisson equations, which are common in some formulations of the incompressible hydrodynamic equations, can be easily and efficiently solved in bounded domains [19]. As a result, to the present day the FC-Gram method has been successfully employed in a wide range of PDE problems [17,20,21,19].…”