A locally stabilized immersed boundary method for the compressible Navier–Stokes equations

Brehm, Christoph; Hader, Christoph; Fasel, Hermann F.

doi:10.1016/j.jcp.2015.04.023

Cited by 95 publications

(44 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Works on viscous compressible flows are still scarce and a few IB methods for viscous compressible flows and acoustic wave propagation problems have been developed . Due to the different mathematical characteristic of the Navier‐Stokes equations for compressible and incompressible flows, there are differences in the implementation of the boundary conditions between these two types of equations as well as in the spatial discretization schemes employed …”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the vast majority of existing IB formulations particularly for viscous compressible flows are up to second‐order accuracy except for the studies by Seo and Mittal and Brehm et al The IBM employed by de Palma et al and de Tullio et al to deal with compressible turbulent flows over a circular cylinder and an airfoil is a direct forcing approach with a linear interpolation and inverse‐distance weighted interpolation, respectively. Even though in the study of de Tullio et al local grid refinement is used, both of these methods lead to locally first‐order accurate approaches.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

Khalili

Larsson²,

Müller

2018

Numerical Methods in Fluids

View full text Add to dashboard Cite

Summary A high‐order immersed boundary method is devised for the compressible Navier‐Stokes equations by employing high‐order summation‐by‐parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high‐order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross‐section of a human upper airway is simulated.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

Khalili

Larsson²,

Müller

2018

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…Their studies show that high-fidelity computations of strong shocked flows can be realised when the solver is augmented with solution-adaptive mesh refinement. 17 A second-order finite-volume (FV) scheme was described and applied to a class of compressible flows in the work of Gorsse et al, 18 whereas the problem of high-order treatment for BCs with emphasis to shocked flows has been addressed in the work of Tan and Shu. There have also been efforts to develop second-order accurate nonconformal solvers for the kinetic equations with application to Euler flows 16 and higher-order finite difference IB schemes for hypersonic flows.…”

Section: Introductionmentioning

confidence: 99%

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

Brahmachary

Natarajan

Kulkarni

et al. 2017

Numerical Methods in Fluids

View full text Add to dashboard Cite

Summary A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.

show abstract

“…[13][14][15] In the current paper, a higher-order sharp immersed boundary method is utilized. The IBM employed for solving the compressible Navier-Stokes equations was discussed in detail in Brehm et al 16 The approach is similar to that described by Li and Ito. 17 To derive a set of linear equations for the coefficients of the boundary stencil the method aims at determining the finite-difference coefficients by minimizing the order of the local truncation error.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper proceeds as follows: first, the immersed boundary method by Brehm et al 16 is briefly described and the additional infrastructure to efficiently deal with unsteady body motion is introduced. Next, a Finite Element Method (FEM) used to simulate the structural dynamics is described and its implementation is validated for simple static deformation and vibration test problems.…”

Section: Introductionmentioning

confidence: 99%

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid-Structure Interaction

Brehm

Barad

Kiris

2016

34th AIAA Applied Aerodynamics Conference

View full text Add to dashboard Cite

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

show abstract

A locally stabilized immersed boundary method for the compressible Navier–Stokes equations

Cited by 95 publications

References 35 publications

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid-Structure Interaction

Contact Info

Product

Resources

About