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Documents published in Scipedia

• Image-based computational hemodynamics methods and their application for the analysis of blood flow past endovascular devices

  J. Cebral, R. Lohner, S. Appanaboyina, C. Putman

  (2007). Biomechanical systems technology, pp. 29-85

  
  

  Abstract

  Knowledge of the hemodynamic conditions in intracranial aneurysms before and after endovascular treatment is important to better understand the mechanisms responsible for aneurysm growth and rupture, and to optimize and personalize the therapies. Unfortunately, there are no reliable imaging techniques for in vivo quantification of blood flow patterns in cerebral aneurysms. Patient-specific, image-based computational models provide an attractive alternative since they can handle any vascular geometry and physiologic flow condition. However, computational modeling of the hemodynamics in cerebral aneurysms after their endovascular treatment is a challenging problem because of the high degree of geometric complexity required to represent and mesh the vascular anatomy and the endovascular devices simultaneously. This paper describes an image-based methodology for constructing patient-specific vascular computational fluid dynamics models and an adaptive grid embedding technique to simulate blood flows around endovascular devices. The methodology is illustrated with several examples ranging from idealized vascular models to patient-specific models of cerebral aneurysms after deployment of stents and coils. These techniques have the potential to be used to select the best therapeutic option for a particular individual and to optimize the design of endovascular devices on a patient-specific basis.

  Abstract
  Knowledge of the hemodynamic conditions in intracranial aneurysms before and after endovascular treatment is important to better understand the mechanisms responsible for [...]

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• A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids

  H. Luo, J. Baum, R. Lohner

  Journal of Computational Physics (2007). Vol. 225 (1), pp. 686-713

  
  

  Abstract

  A weighted essentially non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for the discontinuous Galerkin finite element method on unstructured grids. The solution polynomials are reconstructed using a WENO scheme by taking advantage of handily available and yet valuable information, namely the derivatives, in the context of the discontinuous Galerkin method. The stencils used in the reconstruction involve only the van Neumann neighborhood and are compact and consistent with the DG method. The developed HWENO limiter is implemented and used in a discontinuous Galerkin method to compute a variety of both steady-state and time-accurate compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy, effectiveness, and robustness of the designed HWENO limiter for the DG methods.

  Abstract
  A weighted essentially non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for the discontinuous Galerkin finite [...]

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• Patient-specific modeling of intracranial aneurysmal stenting

  S. Appanaboyina, F. Mut, R. Lohner, C. Putman, J. Cebral

  (2007). Proceedings Volume 6511, Medical Imaging 2007: Physiology, Function, and Structure from Medical

  
  

  Abstract

  Simulating blood flow around stents in intracranial aneurysms is important for designing better stents and to personalize and optimize endovascular stenting procedures in the treatment of these aneurysms. However, the main difficulty lies in the generation of acceptable computational grids inside the blood vessels and around the stents. In this paper, a hybrid method that combines body-fitted grid for the vessel walls and adaptive embedded grids for the stent is presented. Also an algorithm to map a particular stent to the parent vessel is described. These approaches tremendously simplify the simulation of blood flow past these devices. The methodology is evaluated with an idealized stented aneurysm under steady flow conditions and demonstrated in various patient-specific cases under physiologic pulsatile flow conditions. These examples show that the methodology can be used with ease in modeling any patient-specific anatomy and using different stent designs. This paves the way for using these techniques during the planning phase of endovascular stenting interventions, particularly for aneurysms that are difficult to treat with coils or by surgical clipping.

  Abstract
  Simulating blood flow around stents in intracranial aneurysms is important for designing better stents and to personalize and optimize endovascular stenting procedures in [...]

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• A fast, matrix-free implicit method for compressible flows on unstructured grids

  H. Luo, J. Baum, R. Lohner

  (2007). Sixteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 515, pp. 73-78, Springer, Berlin, Heidelberg

  
  

  Abstract

  A fast, matrix-free implicit method has been developed to solve the three dimensional compressible flow problems on unstructured meshes. An approximate system of linear equations arising from the Newton linearization is solved by the GMRES (Generalized Minimum RESidual) algorithm with a LU-SGS (Lower-Upper Symmetric Gauss-Seidel) preconditioner. A remarkable feature of the present GMRES+LU-SGS method is that the storage of the Jacobian matrix can be completely eliminated by approximating the Jacobian with numerical fluxes, resulting in a matrix-free implicit method. The developed method has been used to compute compressible flows around 3D complex aerodynamic configurations for a wide range of flow conditions, from subsonic to supersonic. The numerical results indicate that the use of the GMRES+LU-SGS method leads to a significant increase in performance over the best current implicit methods, GMRES+ILU and LU-SGS, while maintaining memory requirements competitive to its explicit counterpart.

  Abstract
  A fast, matrix-free implicit method has been developed to solve the three dimensional compressible flow problems on unstructured meshes. An approximate system of linear equations [...]

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• A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Euler and Navier-Stokes Equations

  N. Ahmad, Z. Boybeyi, R. Lohner, A. Sarma

  Pure and Applied Geophysics (2007). Vol. 164 (1), pp. 217-244

  
  

  Abstract

  In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the numerical scheme (VAN LEER, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without using explicit filtering for numerical stability.

  Abstract
  In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid [...]

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• Extending the Range and Applicability of the Loose Coupling Approach for FSI Simulations

  R. Lohner, J. Cebral, C. Yang, J. Baum, E. Mestreau, O. Soto

  (2006). Bungartz HJ., Schäfer M. (eds) Fluid-Structure Interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, Heidelberg

  
  

  Abstract

  Several algorithms for fluid-structure interaction are described. All of them are useful for the loose coupling of fluid and structural dynamics codes. The first class of algorithms considers the loose coupling of implicit time-marching codes. Of these, a predictor-corrector algorithm that may be interpreted as a Jacobi iteration with block-diagonal terms was found to be a good compromise of simplicity, generality and speed. The second class of algorithms treats the displacement of the surface of the structure that is in contact with the fluid. It is shown that a straightforward treatment of the displacements for arbitrary choice of timesteps can lead to instabilities. For optimal stability, at each timestep the ending time of the fluid should be just beyond the ending time of the structure. The third class of algorithms treats the movement of the flow mesh in an ALE setting. The use of a projective prediction of mesh velocities, as well as linelet preconditioning for the resulting PCG system can reduce significantly the effort required. Examples are included that show the effectiveness of the proposed procedures.

  Abstract
  Several algorithms for fluid-structure interaction are described. All of them are useful for the loose coupling of fluid and structural dynamics codes. The first class of [...]

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• Generation of viscous grids at ridges and corners

  R. Aubry, R. Lohner

  International Journal for Numerical Methods in Engineering (2007). Vol. 77 (9), pp. 1247-1289

  
  

  Abstract

  An extension of Löhner (AIAA‐93‐3348‐CP , 1993) for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds‐averaged Navier–Stokes computations. Multiple point normals are introduced along ridges and corners. The original technique generates a semi‐structured boundary layer of prismatic elements growing along point normals. Therefore, extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation. The major task of the algorithm consists in recovering conformity in the surface mesh triangulation, which has been lost due to the introduction of the virtual faces. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Each case is highlighted in detail. Special boundary conditions such as symmetry planes and periodic boundary conditions are also handled. Several complex geometries have been chosen to illustrate the proposed procedure, and timings are given, showing that the new module does not place any extra burden on the previous semi‐structured approach.

  Abstract
  An extension of Löhner (AIAA‐93‐3348‐CP , 1993) for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds‐averaged [...]

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• Adaptive Embedded/Immersed Unstructured Grid Techniques

  R. Lohner, J. Cebral, F. Camelli, S. Appanaboyina, J. Baum, E. Mestreau, O. Soto

  Computer Methods in Applied Mechanics and Engineering (2008). Vol. 197 (25-28), pp. 2173-2197

  
  

  Abstract

  Embedded mesh, immersed body or fictitious domain techniques have been used for many years as a way to discretize geometrically complex domains with structured grids. The use of such techniques within adaptive, unstructured grid solvers is relatively recent. The combination of body-fitted functionality for some portion of the domain, together with embedded mesh or immersed body functionality for another portion of the domain offers great advantages, which are increasingly being exploited. The present paper reviews the methodologies pursued so far, addresses implementational issues and shows the possibilities such techniques offer.

  Abstract
  Embedded mesh, immersed body or fictitious domain techniques have been used for many years as a way to discretize geometrically complex domains with structured grids. The [...]

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• Flowfield and Acoustic radiation from imperfectly expanded supersonic jets: Computational Studies

  J. Liu, R. Ramamurti, K. Kailsanath, R. Lohner

  (2007). American Physical Society, 60th Annual Meeting of the Divison of Fluid Dynamics, November 18-20.

  
  

  Abstract

  This project involves the study of sound generated by supersonic jets like those emanating from the exhausts of high-performance military aircraft. This is a joint experimental/computational project with the University of Cincinnati. The flowfield and near-field noise from both convergent and convergent-divergent nozzles have been simulated. The emphasis is on imperfectly expanded or off-design conditions. The impact of grid resolution, initial and boundary conditions on the computed solutions have been assessed. Comparisons with analytical predictions on shock-cell spacing show very good agreement. Comparison to the experimental observations are underway and will be presented at the meeting.

  Abstract
  This project involves the study of sound generated by supersonic jets like those emanating from the exhausts of high-performance military aircraft. This is a joint experimental/computational [...]

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• On the ‘most normal’ normal

  R. Aubry, R. Lohner

  Communications in numerical methods in engineering (2008). Vol. 24 (12), pp. 1641-1652

  
  

  Abstract

  Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes the maximal angle with the given set of normals. A direct application is provided supposing a surface triangulation is available. The set of normals may represent either the face normals of the faces surrounding a point or the point normals of the points surrounding a point. The first algorithm is iterative and straightforward, and is inspired by the one proposed by Pirzadeh (AIAA Paper 94‐0417 , 1994). The second gives more insight into the complete problem as it provides the unique solution explicitly. It would correspond to the general extension of the algorithm presented by Kallinderis (AIAA‐92‐2721 , 1992).

  Abstract
  Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes [...]

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