Stabilized methods for high-speed compressible flows: toward hypersonic simulations

Codoni, David; Moutsanidis, Georgios; Hsu, Ming‐Chen; Bazilevs, Yuri; Johansen, Craig T.; Korobenko, Artem

doi:10.1007/s00466-020-01963-6

Cited by 44 publications

(11 citation statements)

References 74 publications

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“…Here,Resfalse(bold-italicYfalse)=bold-italicA0bold-italicY,t+bold-italicAiadv/pbold-italicY,i+bold-italicAipbold-italicY,i−false(bold-italicKijbold-italicY,jfalse),i−bold-italicAicbold-italicY,iis the residual of the governing equations, τSUPG=bold-italicA0−1timesboldτfalse^SUPG is the stabilizing matrix for the primitive variables, and timesboldτfalse^SUPG is the stabilizing matrix for the conservation variables, which is defined as ( 16 , 17 )timesboldτfalse^SUPG=(4IΔt2+GijA^…”

Section: Methodsmentioning

confidence: 99%

“…Because our simulations are based only on van der Waals’ thermodynamic theory and fundamental continuum mechanics without additional modeling assumptions, we call them direct van der Waals simulations (DVS). Our computations are enabled by a residual-based, stabilized discretization concept that does not require hyperbolicity of the isentropic form of the equations, extends to van der Waals fluids the Streamline Upwind Petrov-Galerkin (SUPG) technique ( 16 , 17 ) and the discontinuity-capturing (DC) operators ( 18 ), and improves the thickened interface methods ( 19 , 20 ). We illustrate the algorithm’s performance with a parametric study of cavitating flow past a cylinder and a simulation of flow over a wedge that shows sheet-to-cloud transition.…”

Section: Introductionmentioning

confidence: 99%

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Direct van der Waals simulation (DVS) of phase-transforming fluids

Wang

Gómez

2023

Sci. Adv.

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We present the method of direct van der Waals simulation (DVS) to study computationally flows with liquid-vapor phase transformations. Our approach is based on a discretization of the Navier-Stokes-Korteweg equations, which couple flow dynamics with van der Waals’ nonequilibrium thermodynamic theory of phase transformations, and opens an opportunity for first-principles simulation of a wide range of boiling and cavitating flows. The proposed algorithm enables unprecedented simulations of the Navier-Stokes-Korteweg equations involving cavitating flows at strongly under-critical conditions and 𝒪(10 5 ) Reynolds number. The proposed technique provides a pathway for a fundamental understanding of phase-transforming flows with multiple applications in science, engineering, and medicine.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct van der Waals simulation (DVS) of phase-transforming fluids

Wang

Gómez

2023

Sci. Adv.

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“…Over the years since their inception, the ST-SUPS, ALE-SUPS, RBVMS, ALE-VMS, and ST-VMS have become a powerful set of computational methods and have been applied to some of the most challenging classes of flow problems. The classes of problems computed with the ALE-SUPS, RBVMS, and ALE-VMS include parachutes [12], wind turbines [26]-[47], medical applications [13], [48]- [61], free-surface flows [62]- [66], aircraft applications [67,68], turbomachinery [69]-[75], marine applications [76]- [78], bridges [79]- [83], stratified flows [84,85], hypersonic flows [86], two-phase flows [87]- [93], additive manufacturing [94], immersogeometric FSI and flow analysis [95]- [99], and mixed ALE-VMS/Immersogeometric computations [57]- [59], [100]- [108] in the framework of the FSITICT. A comprehensive summary of the classes of flow problems computed with ST-SUPS and ST-VMS prior to July 2018 was provided in [109].…”

Section: Thementioning

confidence: 99%

Mesh Moving Methods in Flow Computations with the Space–Time and Arbitrary Lagrangian–Eulerian Methods

Takizawa

Bazilevs

Tezduyar

2022

J. ADV. ENG. COMPUT.

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A good mesh moving method is an important part of ﬂow computations with moving-mesh methods like the space–time (ST) and Arbitrary Lagrangian–Eulerian (ALE) methods. With a good mesh moving method, we can decrease the remeshing frequency even when the ﬂuid–solid and ﬂuid–ﬂuid interfaces undergo large displacements, decrease the element distortion in parts of the ﬂow domain where we care about the solution accuracy more, and maintain the quality of the boundary layer meshes near the ﬂuid–solid interfaces as the mesh moves to follow those interfaces. Since 1990, quite a few good mesh moving methods have been developed for use with the ST computational methods, from the mesh Jacobian-based stiﬀening to a mesh moving method based on fiber-reinforced hyperelasticity to a linear-elasticity mesh moving method with no cycle-to-cycle accumulated distortion. These methods have been used in computation of many complex ﬂow problems in the categories of ﬂuid–particle interaction, ﬂuid–structure interaction, and more generally, moving boundaries and interfaces. The computations were with both the ST and ALE methods. We provide an overview of these methods and present examples of the computations performed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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“…The classes of problems computed with the ALE-SUPS, RBVMS, and ALE-VMS include wind turbines , turbomachinery [60][61][62][63][64][65][66], stratified flows [67,68], bridges [69][70][71][72][73], marine applications [74][75][76], free-surface flows [77][78][79][80][81], two-phase flows [82][83][84][85][86][87][88], additive manufacturing [89], aircraft applications [90,91], hypersonic flows [92], parachutes [33], cardiovascular medicine [34,[93][94][95][96][97][98][99][100][101][102][103][104][105][106], mixed ALE-VMS immersogeometric analysis ...…”

Section: Introductionmentioning

confidence: 99%

High-resolution multi-domain space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation

Kuraishi

Takizawa

et al. 2022

Comput Mech

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We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.

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Stabilized methods for high-speed compressible flows: toward hypersonic simulations

Cited by 44 publications

References 74 publications

Direct van der Waals simulation (DVS) of phase-transforming fluids

Direct van der Waals simulation (DVS) of phase-transforming fluids

Mesh Moving Methods in Flow Computations with the Space–Time and Arbitrary Lagrangian–Eulerian Methods

High-resolution multi-domain space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation

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