The computational efficiency of non-linear frequency domain methods

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

“…In Sect. 3.4.1, we give a semi-implicit formulation of our method which allows for solving (47) using a GSI method, similar to pseudo-time methods discussed in [12,31,41] and GSI method literature (e.g., see [11,25], and [52]). Using this formulation, we present a new form of adaptivity in Sect.…”

“…Because the method requires little extra effort to implement, it can conceivably be used to improve performance in existing computational frameworks with a minimum of reprogramming. We note that NAGSI's convergence could be accelerated by combining it with multigrid techniques (e.g., such as those used for iterative techniques in computational fluid dynamics problems by [12,31], and [41]) by implementing NAGSI at each level of the multigrid technique. Lastly, we note that while we have focused our adaptivity approach on improving performance on fixed, regular grids, we believe it is possible to apply a similar philosophy to irregular grids by choosing local discretizations that can be applied to selected mesh points for improved performance.…”

“…The case of discretizing [D∇p · n] at a point (x i − θΔx, y j ) is completely analogous, and the discretization in the y-direction is identical. In the 3-D case, we would proceed similarly by defining third basis vectors such as (41) This method has several advantages. In the spirit of the ghost cell method, the new stencil can be expressed entirely in terms of computational grid points and the jump interface location.…”

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

“…Accordingly, the accuracy of the solution is dependent on the number of harmonics used as well as the level of unsteadiness in the flow. Further work demonstrated thoroughly the increased efficiency and excellent accuracy provided by frequency-domain methods in comparison with typical time-accurate approaches [43,51,53,63]. In addition to the reduced number of time instances, the computation of the initial transient flow behavior that is usually necessary in a typical time-accurate framework is discarded due to the direct convergence of frequency-domain methods to the final periodic solution.…”

Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization

“…In an extension of this work, Ekici and Hall [43] applied the technique, known as the harmonic balance technique, to multistage turbomachinery applications where a variety of frequencies may be present. Other spectral methods have been demonstrated by McMullen et al [44,45] (the nonlinear frequency domain (NLFD) method) and Gopinath and Jameson [46] (the time-spectral method). The main differences between the methods are the portions of the solution that are computed in the frequency and time domains.…”