Publications
Preprints
- Chu, T., Wilfong, B., Koehler, T., McMullen, R. M., & Bryngelson, S. H. (2026). Coupled Rayleigh–Taylor and Faraday instabilities in vertically vibrated cylindrical containers. In arXiv preprint arXiv:2607.28932.
@unpublished{chu2026coupled, title = {Coupled Rayleigh--Taylor and Faraday instabilities in vertically vibrated cylindrical containers}, author = {{Chu, T.} and Wilfong, Benjamin and Koehler, Timothy and McMullen, Ryan M and Bryngelson, Spencer H}, journal = {arXiv preprint arXiv:2607.28932}, year = {2026} } - Chu, T., Beckett, J., Zhu, Z., Estrada, J. B., & Bryngelson, S. H. (2026). Limits of constant-parameter constitutive models for hydrogels under inertial cavitation. In arXiv preprint arXiv:2606.13584.
@unpublished{chu2026limits, title = {Limits of constant-parameter constitutive models for hydrogels under inertial cavitation}, author = {{Chu, T.} and Beckett, Joseph and Zhu, Zhiren and Estrada, Jonathan B and Bryngelson, Spencer H}, journal = {arXiv preprint arXiv:2606.13584}, year = {2026} }
Refereed Journal Articles
- *Yu, H., *Chu, T., & Bryngelson, S. H. (2026). Energy dissipation mechanisms in an acoustically-driven slit. Journal of Fluid Mechanics, 1040, A47. *Equal contribution.
@article{yu2026energy, title = {Energy dissipation mechanisms in an acoustically-driven slit}, author = {*Yu, Haocheng and {*Chu, T.} and Bryngelson, Spencer H}, note = {*Equal contribution.}, journal = {Journal of Fluid Mechanics}, year = {2026}, doi = {doi:10.1017/jfm.2026.11896}, volume = {1040}, page = {A47} }We quantify the conversion of incident acoustic energy into vortical motion and viscous dissipation for a plane wave passing through large-aspect-ratio slit geometries. We perform direct numerical simulations over a broad imposed parameter space in incident sound pressure level (ISPL), Strouhal number (\St), and Reynolds number (\Rey). Spectral proper orthogonal decomposition (SPOD) yields energy-ranked coherent structures at each frequency, from which we construct mode-by-mode fields for spectral kinetic energy (KE) and viscous loss (VL) to examine the acoustic absorption mechanisms. At \mathrmISPL = \SI150\decibel, the acoustic–hydrodynamic energy conversion is highest when \St \le 4\St_0, corresponding to an effective Keulegan–Carpenter number (\Kc) larger than 40. In this regime, three-dimensional simulations show that the dominant flow response is two-dimensional, with the oscillatory shear layer near the slit corners rolling up into shedding vortices. VL accounts for \SIrange[]2060\percent of the KE contribution. For larger \St, the Stokes-layer confinement produces X-shaped near-slit modes, reducing the energy input by approximately \SI50\percent. The influence of \Rey depends on amplitude. Larger \Rey corresponds to suppressed broadband fluctuations and sharpened harmonic peaks at \SI150\decibel. At \mathrmISPL = \SI120\decibel, the boundary layers remain attached, vortex shedding is weak, absorption monotonically scales with viscosity, and the \Rey- and \St-dependencies become comparable. Across all conditions, more than \SI99\percent of the VL is confined to a compact region surrounding the slit mouth. The KE–VL spectra identify regimes that enhance or suppress acoustic damping in slit geometries, providing a physically interpretable basis for acoustic-based design.
- Chu, T., Estrada, J. B., & Bryngelson, S. H. (2026). Accelerating Bayesian Optimal Experimental Design via Local Radial Basis Functions: Application to Soft Material Characterization. Journal of Computational Physics, 562, 115002.
@article{chu2026accelerating, title = {Accelerating Bayesian Optimal Experimental Design via Local Radial Basis Functions: Application to Soft Material Characterization}, author = {{Chu, T.} and Estrada, Jonathan B and Bryngelson, Spencer H}, journal = {Journal of Computational Physics}, year = {2026}, volume = {562}, pages = {115002}, doi = {10.1016/j.jcp.2026.115002} }We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The RBF–BOED method uses RBFs’ ability to handle scattered parameter points, a property that aligns naturally with the probabilistic sampling inherent to Bayesian methods. By constructing accurate deterministic surrogates from local neighborhood information, the method enables high-order approximations with reduced computational overhead. As a result, computing the expected information gain (EIG) requires evaluating only a small uniformly sampled subset of prior parameter values, greatly reducing the number of expensive forward-model simulations needed. For demonstration, we apply RBF–BOED to optimize a laser-induced cavitation (LIC) experimental setup, in which forward simulations based on inertial microcavitation rheometry (IMR) characterize the viscoelastic properties of hydrogels. The underlying highly nonlinear bubble-dynamics model exemplifies the practical challenges encountered in BOED applications. Two experimental design scenarios, single- and multi-constitutive-model problems, are explored. Results show that EIG estimates can be obtained at just 8% of the full computational cost in a five-model problem within a two-dimensional design space. This advance offers a scalable approach to optimal experimental design for soft and biological materials.
- *Yeung, B., *Chu, T., & Schmidt, O. T. (2026). Triadic orthogonal decomposition reveals nonlinearity in fluid flows. Journal of Fluid Mechanics, 1031, A34. *Equal contribution.
@article{yeung2026triadic, title = {Triadic orthogonal decomposition reveals nonlinearity in fluid flows}, author = {*Yeung, Brandon and {*Chu, T.} and Schmidt, Oliver T}, journal = {Journal of Fluid Mechanics}, volume = {1031}, pages = {A34}, year = {2026}, doi = {10.1017/jfm.2026.11183}, note = {*Equal contribution.}, publisher = {Cambridge University Press} }Energy transfer across scales is fundamental in fluid dynamics, linking large-scale flow motions to small-scale turbulent structures in engineering and natural environments. Triadic interactions among three wave components form complex networks across scales, challenging understanding and model reduction. We introduce triadic orthogonal decomposition (TOD), a method that identifies coherent flow structures optimally capturing spectral momentum transfer, quantifies their coupling and energy exchange in an energy-budget bispectrum and reveals the regions where they interact. Triadic orthogonal decomposition distinguishes three components – a momentum recipient, donor and catalyst – and recovers laws governing pairwise, six-triad and global triad conservation. We apply TOD to three examples: the classical cylinder wake, experimental wind turbine wake data and a direct numerical simulation of isotropic turbulence. Energy transfer can be spatially distributed but vanish upon integration or spatially localised but facilitate net interscale exchange, so a complete characterisation of nonlinearity requires examination of both integral and local transfers. In the cylinder wake, we link backscatter of energy from high to low frequencies to a compact attenuation region downstream of the cylinder. In the turbine wake, we confirm the known association between energy amplification and decay and vortex tilting, but observe more complex secondary mechanisms in suboptimal modes. For isotropic turbulence, we derive and confirm inertial-range frequency scaling for convective–recipient covariances, then demonstrate self-similar energy transfer at each rank.
- Chu, T., & Schmidt, O. T. (2025). Stochastic reduced-order Koopman model for turbulent flows. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481(2323).
@article{chu2025stochastic, title = {Stochastic reduced-order Koopman model for turbulent flows}, author = {{Chu, T.} and Schmidt, Oliver T}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {481}, number = {2323}, year = {2025}, publisher = {The Royal Society}, doi = {10.1098/rspa.2025.0270} }A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated convolutional Koopman model accurately forecasts short-time transient dynamics while preserving long-term statistical properties. A discrete Koopman operator is used to evolve convolutional coordinates that govern the temporal dynamics of spectral orthogonal modes, which, in turn, represent the energetically most salient large-scale coherent flow structures. Turbulence closure is achieved in two steps: first, by inflating the convolutional coordinates to incorporate nonlinear interactions between different scales, and second, by modelling the residual error as a stochastic source. An empirical dewhitening filter informed by the data is used to maintain the second-order flow statistics. The model uncertainty is quantified through either Monte–Carlo simulation or by directly propagating the model covariance matrix. The model is demonstrated on the Ginzburg–Landau equations, large-eddy simulation data of a turbulent jet, and particle image velocimetry data of the flow over an open cavity. In all cases, the model is predictive over time horizons indicated by a detailed error analysis and integrates stably over arbitrary time horizons, generating realistic surrogate data.
- Chu, T., Wilfong, B., Koehler, T., McMullen, R. M., & Bryngelson, S. H. (2025). Competing mechanisms at vibrated interfaces of density-contrast fluids. Physical Review Fluids, 10(9), 093904.
@article{chu2025competing, title = {Competing mechanisms at vibrated interfaces of density-contrast fluids}, author = {{Chu, T.} and Wilfong, Benjamin and Koehler, Timothy and McMullen, Ryan M and Bryngelson, Spencer H}, journal = {Physical Review Fluids}, volume = {10}, number = {9}, pages = {093904}, year = {2025}, publisher = {APS}, doi = {10.1103/r9b3-psg4} }Fluid-fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. The hydrodynamic instability of fluid interfaces has long centered on the pressure gradient-driven long-wavelength Rayleigh-Taylor instability and the resonance-induced short-wavelength Faraday instability. However, neither instability alone can explain the dynamics when both mechanisms are present. We identify a previously unseen multi-modal instability emerging from their coexistence. When the denser fluid is polydimethylsiloxane, the mixed region at a high density contrast (Atwood number = 0.9) spans a vibration amplitude range approximately twice the gravitational acceleration. Using Floquet stability analysis, we show how vibrations govern transitions between the RT and Faraday instabilities, leading to contention between these instabilities rather than resonant enhancement. The initial transient growth is represented by the exponential modal growth of the most unstable Floquet exponent, along with its accompanying periodic behavior. Direct numerical simulations validate these findings and track interface breakup into the multiscale and nonlinear regimes. Specifically, we show that growing RT modes nonlinearly suppresses Faraday responses even when the initial growth rate of the Faraday instability is 3.63 times that of RT, so a bidirectional competition hinders their sustained coexistence.
- Chu, T., Estrada, J. B., & Bryngelson, S. H. (2025). Bayesian optimal design accelerates discovery of soft material properties from bubble dynamics. Computational Mechanics, 76(2), 431–447.
@article{chu2025bayesian, title = {Bayesian optimal design accelerates discovery of soft material properties from bubble dynamics}, author = {{Chu, T.} and Estrada, Jonathan B and Bryngelson, Spencer H}, journal = {Computational Mechanics}, volume = {76}, number = {2}, pages = {431--447}, year = {2025}, publisher = {Springer}, doi = {10.1007/s00466-025-02606-4} }An optimal sequential experimental design approach is developed to computationally characterize soft material properties at the high strain rates associated with bubble cavitation. The approach involves optimal design and model inference. The optimal design strategy maximizes the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown soft material properties. We infer constitutive models by characterizing the associated viscoelastic properties from measurements via a hybrid ensemble-based 4D-Var method (En4D-Var). The inertial microcavitation-based high strain-rate rheometry (IMR) method (Estrada et al. J Mech Phys Solids 112:291–317, 2018) simulates the bubble dynamics under laser-induced cavitation. We use experimental measurements to create synthetic data representing the viscoelastic behavior of stiff and soft polyacrylamide hydrogels under realistic uncertainties. The synthetic data are seeded with larger errors than state-of-the-art measurements yet matches known material properties, reaching relative error within 10 sequential designs (experiments). We discern between two seemingly equally plausible constitutive models, Neo-Hookean Kelvin–Voigt and quadratic Kelvin–Voigt, with a probability of correctness larger than in the same number of experiments. This strategy discovers soft material properties, including discriminating between constitutive models and discerning their parameters, using only a few experiments.
- Chu, T., & Schmidt, O. T. (2024). Mesh-free hydrodynamic stability. Journal of Computational Physics, 502, 112822.
@article{chu2024mesh, title = {Mesh-free hydrodynamic stability}, author = {{Chu, T.} and Schmidt, Oliver T}, journal = {Journal of Computational Physics}, volume = {502}, pages = {112822}, year = {2024}, publisher = {Elsevier}, doi = {10.1016/j.jcp.2024.112822} }A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline functions with polynomial augmentation (PHS+poly) are used to construct the discrete linearized incompressible and compressible Navier-Stokes operators on scattered nodes. Rigorous global and local eigenvalue stability studies of these global operators and their constituent RBF stencils provide a set of parameters that guarantee stability without the need for hyperviscosity or other ad hoc regularizations, while balancing accuracy and computational efficiency. Specialized elliptical stencils to compute boundary-normal derivatives are introduced, and the treatment of reflectional and rotational symmetries is discussed. In particular, treating the pole singularity in cylindrical coordinates permits dimensionality reduction from 3D to 2D in rotational flows like jets. The numerical framework is demonstrated and validated on several hydrodynamic stability methods ranging from classical linear theory of laminar flows to state-of-the-art non-modal approaches that are applicable to turbulent mean flows. The examples include linear stability, resolvent, and wavemaker analyses of cylinder flow at Reynolds numbers ranging from 47 to 180, and resolvent and wavemaker analyses of the self-similar flat-plate boundary layer at a Reynolds number as well as the turbulent mean of a high-Reynolds-number transonic jet at Mach number 0.9. All previously-known results are found in close agreement with the literature. Finally, the resolvent-based wavemaker analyses of the Blasius boundary layer and turbulent jet flows offer new physical insight into the modal and non-modal growth in these flows.
- Chu, T., & Schmidt, O. T. (2023). RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes. Journal of Computational Physics, 474, 111756.
@article{chu2023rbf, title = {RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes}, author = {{Chu, T.} and Schmidt, Oliver T}, journal = {Journal of Computational Physics}, volume = {474}, pages = {111756}, year = {2023}, publisher = {Elsevier}, doi = {10.1016/j.jcp.2022.111756} }A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial augmentation (PHS+poly) are used to construct the global differentiation matrices. A systematic parameter study identifies a combination of stencil size, PHS exponent, and polynomial degree that minimizes the truncation error for a wave-like test function on scattered nodes. Classical modified wavenumber analysis is extended to RBF-FDs on heterogeneous node distributions and used to confirm that the accuracy of the selected 28-point stencil is comparable to that of spectral-like, 6th-order Padé-type finite differences. The Navier-Stokes solver is demonstrated on two benchmark problems, internal flow in a lid-driven cavity in the Reynolds number regime 10^2 ≤\mathrmRe≤10^4, and open flow around a cylinder at \mathrmRe= 100 and 200. The combination of grid staggering and careful parameter selection facilitates accurate and stable simulations at significantly lower resolutions than previously reported, using more compact RBF-FD stencils, without special treatment near solid walls, and without the need for hyperviscosity or other means of regularization.
- Llewellyn Smith, S. G., Chu, T., & Hu, Z. (2022). Equations of motion for weakly compressible point vortices. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2226).
@article{llewellyn2022equations, title = {Equations of motion for weakly compressible point vortices}, author = {Llewellyn Smith, Stefan G and {Chu, T.} and Hu, Z}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {380}, number = {2226}, year = {2022}, publisher = {The Royal Society}, doi = {10.1098/rsta.2021.0052} }Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, M, using a Rayleigh–Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales O(M^2logM) and O(M^2). Examples are given for co-rotating and co-propagating vortex pairs. The former show a correction to the rotation rate and, in general, to the centre and radius of rotation, while the latter recover the known result that the steady propagation velocity is unchanged. For unsteady configurations, the vortex solution matches to a far field in which acoustic waves are radiated.
- Chu, T., & Schmidt, O. T. (2021). A stochastic SPOD-Galerkin model for broadband turbulent flows. Theoretical and Computational Fluid Dynamics, 35(6), 759–782.
@article{chu2021stochastic, title = {A stochastic SPOD-Galerkin model for broadband turbulent flows}, author = {{Chu, T.} and Schmidt, Oliver T}, journal = {Theoretical and Computational Fluid Dynamics}, volume = {35}, number = {6}, pages = {759--782}, year = {2021}, publisher = {Springer}, doi = {10.1007/s00162-021-00588-6} }The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number and Reynolds number Re=10e6.
- Chu, T., & Llewellyn Smith, S. G. (2021). Helical contour dynamics. Regular and Chaotic Dynamics, 26(6), 600–617.
@article{chu2021helical, title = {Helical contour dynamics}, author = {{Chu, T.} and Llewellyn Smith, Stefan G}, journal = {Regular and Chaotic Dynamics}, volume = {26}, number = {6}, pages = {600--617}, year = {2021}, publisher = {Springer}, doi = {10.1134/S1560354721060022} }The equations of motion for an incompressible flow with helical symmetry (invariance under combined axial translation and rotation) can be expressed as nonlinear evolution laws for two scalars: vorticity and along-helix velocity. A metric term related to the pitch of the helix enters these equations, which reduce to two-dimensional and axisymmetric dynamics in appropriate limits. We take the vorticity and along-helix velocity component to be piecewise constant. In addition to this vortex patch, a vortex sheet develops when the along-helix velocity is nonzero. We obtain a contour dynamics formulation of the full nonlinear equations of motion, in which the motion of the boundary is computed in a Lagrangian fashion and the velocity field can be expressed as contour integrals, reducing the dimensionality of the computation. We investigate the stability properties of a circular vortex patch along the axis of the helix in the presence of a vortex sheet and along-helix velocity. A linear stability calculation shows that the system is stable when the initial vortex sheet is zero, but can be stable or unstable in the presence of a vortex sheet. Using contour dynamics, we examine the nonlinear evolution of the system, and show that nonlinear effects become important in unstable cases.
- Llewellyn Smith, S. G., Chang, C., Chu, T., Blyth, M., Hattori, Y., & Salman, H. (2018). Generalized contour dynamics: A review. Regular and Chaotic Dynamics, 23(5), 507–518.
@article{llewellyn2018generalized, title = {Generalized contour dynamics: A review}, author = {Llewellyn Smith, Stefan G and Chang, Ching and {Chu, T.} and Blyth, Mark and Hattori, Yuji and Salman, Hayder}, journal = {Regular and Chaotic Dynamics}, volume = {23}, number = {5}, pages = {507--518}, year = {2018}, publisher = {Springer}, doi = {10.1134/S1560354718050027} }Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow.
Refereed Conference Proceedings
- Chu, T., Yeung, B., & Schmidt, O. T. (2024). An orthogonal decomposition for nonlinear modal analysis. AIAA AVIATION FORUM AND ASCEND 2024, 4187.
@inproceedings{chu2024orthogonal, title = {An orthogonal decomposition for nonlinear modal analysis}, author = {{Chu, T.} and Yeung, Brandon and Schmidt, Oliver T}, booktitle = {AIAA AVIATION FORUM AND ASCEND 2024}, pages = {4187}, year = {2024}, doi = {arc.aiaa.org/doi/10.2514/6.2024-4187} }An orthogonal modal decomposition for identifying triadic interactions in fluid flows is presented. The decomposition is based on spectral momentum transfer and extracts coherent structures that partake in three-wave interactions and are optimal in terms of the third-order space-time flow statistics. The method distinguishes between two quadratically interacting components, one acting as a catalyst and the other as a donor of momentum, that collectively contribute to a tertiary component, the recipient. The resulting modes maximize the covariance between the donor and recipient for each triad. The method can be understood as an extension of bispectral mode decomposition (BMD) by considering the exact form of the quadratic nonlinearity of the Navier-Stokes equations. Unlike BMD, and more similar to classical proper orthogonal decomposition (POD), it provides ranked bases for the donor and recipient that are jointly optimal and orthonormal in their respective inner products. Two applications are considered: numerical data of a canonical unsteady cylinder wake and experimental data of a turbulent wind turbine wake by Biswas and Buxton (JFM, 2024).
- Chu, T., & Schmidt, O. T. (2023). RBF-FD-based global resolvent analysis: the Blasius boundary layer. AIAA AVIATION 2023 Forum, 3567.
@inproceedings{chu2023rbg, title = {RBF-FD-based global resolvent analysis: the Blasius boundary layer}, author = {{Chu, T.} and Schmidt, Oliver T}, booktitle = {AIAA AVIATION 2023 Forum}, pages = {3567}, year = {2023}, doi = {10.2514/6.2023-3567} }A high-order mesh-free hydrodynamic stability analysis framework is developed based on radial basis function-based finite differences (RBF-FD). The global linearized Navier-Stokes operator is discretized using polyharmonic spline RBFs with polynomial augmentation (PHS+poly). As a validation test case, the non-parallel flat-plate boundary layer within a computational domain corresponding to a local Reynolds number of 0 ≤ Re_x ≤ 6x10^5 is considered. The computational domain is discretized using scattered nodes created by an unstructured mesh generator. The discrete resolvent operator is constructed, and its singular components are analyzed. The resulting optimal response modes are identified as Tollmien-Schlichting (TS) wavepackets. These responses are optimally forced by the upstream tilted structures that leverage the Orr mechanism. Favorable comparisons to previous literature, both qualitatively and quantitatively, validate the novel framework.
- Chu, T., & Schmidt, O. T. (2022). Mesh-free RBF-based discretizations for hydrodynamic stability analysis. AIAA AVIATION 2022 Forum, 4098.
@inproceedings{chu2022mesh, title = {Mesh-free RBF-based discretizations for hydrodynamic stability analysis}, author = {{Chu, T.} and Schmidt, Oliver T}, booktitle = {AIAA AVIATION 2022 Forum}, pages = {4098}, year = {2022}, doi = {10.2514/6.2022-4098} }Radial basis function-based finite differences (RBF-FD) are used to develop a high-order mesh-free hydrodynamic stability analysis tool for complex geometries. Polyharmonic spline RBFs with polynomial augmentation (PHS+poly) are used to construct the discrete linearized Navier-Stokes and resolvent operators on arbitrarily scattered nodes. The PHS+poly discretization is shown to yield accurate, stable, and computationally efficient discretizations of the large hydrodynamic stability matrix problems arising in two-dimensional classical linear theory and resolvent analysis. The mean-flow stability of the wake behind a cylinder in the vicinity of the critical point is studied using both theories. The predicted flow instabilities, including the vortex shedding frequency and associated coherent structures, closely match those reported in the literature.
- Chu, T., & Schmidt, O. (2021). An RBF-based finite difference discretization of the Navier-Stokes equations: error analysis and application to lid-driven cavity flow. AIAA AVIATION 2021 FORUM, 2743.
@inproceedings{chu2021rbf, title = {An RBF-based finite difference discretization of the Navier-Stokes equations: error analysis and application to lid-driven cavity flow}, author = {{Chu, T.} and Schmidt, Oliver}, booktitle = {AIAA AVIATION 2021 FORUM}, pages = {2743}, year = {2021}, doi = {10.2514/6.2021-2743} }Radial basis function-finite differences (RBF-FD) are used to solve the incompressible Navier-Stokes equations on scattered nodes. We present a semi-implicit fractional-step method that uses a staggered grid arrangement. The RBF-QR method devised by Fornberg and Piret[1] is used to obtain the RBF-FD weights for the spatial derivatives. We propose a rigorous error analysis strategy to identify optimal combinations of the shape parameter, ε, and the stencil size,n. A modified wavenumber analysis shows that the accuracy of the RBF differentiation matrices based on the optimal parameters is comparable to 4th-order Padé-type finite differences, for both first and second derivatives. The internal flow in a lid-driven cavity is studied as an example. We demonstrate that stable solutions are obtained without the need for hyperviscosity.