Moretti's Shock-Fitting Methods on Structured and Unstructured Meshes

Bonfiglioli, Aldo; Paciorri, Renato; Nasuti, Francesco; Onofri, Marcello

doi:10.1016/bs.hna.2016.09.011

Cited by 5 publications

(5 citation statements)

References 44 publications

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“…For an overview of front-tracking methods, see [47]. For an overview of Moretti's shock-fitting methods, see [48].…”

Section: Alternative Methods For Shock Capturing-front-tracking Metho...mentioning

confidence: 99%

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Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

Yee,

Sjögreen

2024

Fluids

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This comprehensive overview presents our continued efforts in high-order finite difference method (FDM) development for adaptive numerical dissipation control in the long-time integration of direct numerical simulation (DNS), large eddy simulation (LES), and implicit LES (ILES) computations of compressible turbulence for gas dynamics and MHD. The focus is on turbulence with shock wave numerical simulations using the adaptive blending of high-order structure-preserving non-dissipative methods (classical central, Padé (compact), and dispersion relation-preserving (DRP)) with high-order shock-capturing methods in such a way that high-order shock-capturing methods are active only in the vicinity of shock/shear waves, and high-gradient and spurious high-frequency oscillation regions guided via flow sensors. Any efficient and high-resolution high-order shock-capturing methods are good candidates for the blending of methods procedure. Typically, the adaptive blending of more than one method falls under two camps: hybrid methods and nonlinear filter methods. They are applicable to unstructured finite volume, finite element, discontinuous Galerkin, and spectral element methods. This work represents the culmination of over 20 years of high-order FDM developments and hands-on experience by the authors and collaborators in adaptive numerical dissipation control using the “high order nonlinear filter approach”. Extensions of these FDM versions to curvilinear nonuniform, freestream-preserving moving grids and time-varying deforming grids were also developed. By examining the construction of these two approaches using the high-order multistage type of temporal discretization, the nonlinear filter approach is made more efficient and less CPU-intensive while obtaining similar accuracy. A representative variety of test cases that compare the various blending of high-order methods with standalone standard methods is illustrated. Due to the fact that our nonlinear filter methods are not well known in compressible turbulence with shock waves, the intent of this comprehensive overview is for general audiences who are not familiar with our nonlinear filter methods. For readers interested in the implementation of our methods into their computer code, it is hoped that the long overview will be helpful.

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“…For an overview of front-tracking methods, see [47]. For an overview of Moretti's shock-fitting methods, see [48].…”

Section: Alternative Methods For Shock Capturing-front-tracking Metho...mentioning

confidence: 99%

“…j−1/2 )/∆x. If a numerical example can be found where (48) does not hold, then clearly, KEP cannot hold. If (48) seems to hold numerically, the test is inconclusive.…”

Section: Kinetic Energy-preserving (Kep) Propertymentioning

confidence: 99%

Numerical Dissipation Control in High-Order Methods for Compressible Turbulence: Recent Development

Yee,

Sjögreen

2024

Fluids

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“…Flow conditions on the upper boundary are set to represent the accurate movement of the shock wave. In all following simulations, physical time is 0.2s , 0.6 CFL  , block max level is 2 with refinement ratio (4,2) . The initial condition of primitive state variables is The first group of experiments is to test the parallel scalability of the current AMR code.…”

Section: Double Mach Reflection Of a Strong Shockmentioning

confidence: 99%

“…The advantage of a shock-fitting method is its accuracy in smooth regions and saving of computational cost. On the other hand, the location of a discontinuity in three-dimensional flows containing complex interactions is not easy to find which restricts the application of shock-fitting methods [2].…”

Section: Introductionmentioning

confidence: 99%

Efficient Shock Capturing Based on Parallel Adaptive Mesh Refinement Framework

Xia

2022

J. Phys.: Conf. Ser.

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Based on AMReX, a software framework for massively parallel, block-structured adaptive mesh refinement (AMR) applications and in combination with finite difference weighted essential non-oscillatory (WENO) method, a numerical procedure is developed to provide universal discontinuity capturing capability for inviscid, compressible flow. Test cases of one-dimensional and two-dimensional flows containing shock waves, contact discontinuities, flow instabilities, and their interactions are considered to validate the high resolution of AMR for characteristic flow structure under unsteady conditions. The current elaborate AMR-based code is proven to have superior efficiency relative to global refinement via experiments including different initial mesh intervals, refinement ratios at all levels, and. Evidence in executions with multiple processes and domain division sizes indicates its high parallel scalability. Thus, the application built on AMReX is promising for simulations of phenomena undergoing rapid local variation such as compressible turbulence and multiphase interactions.

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“…According to the criteria suggested in literature (Marshall, 2003) Gustaffson et al (1991) for all flow solvers using adaptive techniques. As recent studies surveyed (Gustaffson et al, 1991;Désidéri et al, 1991;De Zeeuw and Powell, 1993;Balakrishnan and Yousuf, 2017;Satofuka et al, 1993;Bonfiglioli et al, 2016) currently proposed, solution-adapted Cartesian technique was not used for viscous flow. However, the geometric and solution-adaptive Cartesian grid solution techniques not only help to accelerate the solution, but also ensure that the residuals are kept at low levels, that are, increasing the accuracy of the solution.…”

mentioning

confidence: 99%