Georgios N. Lygidakis

Using the Finite-Volume Method and Hybrid Unstructured Meshes to Compute Radiative Heat Transfer in 3-D Geometries

In this work an algorithm using the finite-volume method is presented for the parallelized computation of radiative heat transfer for absorbing, emitting, and either isotropically or anisotropically scattering gray media. Attention is mainly toward the extension of the finite-volume methodology to hybrid unstructured meshes, using a node-centered median-dual approach, with highly stretched elements at the solid wall regions, and the evaluation of its effectiveness and accuracy in such girds. As the parallelized calculation and the utilization of hybrid meshes are not common, results of the present algorithm against benchmark problems are used to demonstrate their equal potential.

Using a High-Order Spatial/Temporal Scheme and Grid Adaptation with a Finite-Volume Method for Radiative Heat Transfer

In this work an algorithm using the finite-volume method along with a second-order-accurate spatial/temporal scheme and the h-refinement technique is evaluated in the parallelized computation of radiative heat transfer in absorbing-emitting and scattering gray media. The second-order spatial scheme is based on the reconstruction of radiative intensitys values, jointed with a slope limiter to maintain monotonicity. Additionally, the h-refinement method is incorporated to enrich targeted areas of the mesh during the solution procedure. The numerical results reveal the mitigation of false scattering and consequently the improvement of accuracy, employing these techniques in coarse unstructured hybrid grids.

Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation—Part I: Methodology

A parallel spatial/angular agglomeration multigrid scheme is developed to accelerate the finite-volume method (FVM) for the computation of radiative heat transfer in absorbing, emitting, and scattering gray media. The multigrid scheme is based on the solution of the radiative transfer equation (RTE) with the full approximation scheme (FAS) on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of the adjacent control volumes and control angles, respectively. The numerical tests reveal the improvement of efficiency employing the aforementioned technique, especially in cases considering scattering media and reflecting boundaries.

Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation—Part II: Numerical Results

A parallel spatial/angular agglomeration multigrid methodology, employing the full approximation scheme (FAS), is developed to accelerate the finite-volume method for the prediction of radiative heat transfer in absorbing, emitting, and scattering gray media. The methodology for the spatial, angular, and combined spatial/angular agglomeration multigrid procedure was analyzed in Part I of this study. In this second part the proposed numerical scheme is validated against benchmark test cases, demonstrating its capability for considerably improved computational performance, especially in problems including scattering media and reflecting boundaries.

A Parallelized Node-Centered Finite Volume Method for Computing Radiative Heat Transfer on 3D Unstructured Hybrid Grids

An algorithm for the computation of radiative heat transfer for absorbing, emitting and either isotropically or anisotropically scattering gray medium in three dimensions is developed. Radiative transfer equation is solved using a node-centered finite volume method in combination with an edge-based data structure, while scattering phase function is defined by Legendre polynomial expansions. Hybrid unstructured grids are used, due to their good viscous layer resolving capability, considering that our final objective is the analysis of coupled heat transfer-fluid flow problems. In addition, domain decomposition approach with message passing interface model is utilized, in order the proposed algorithm to be implemented in a parallel computational system. Numerical results reveal that the present methodology has a good performance in terms of accuracy, geometric flexibility, and computational efficiency.Copyright

Assessment of different spatial/angular agglomeration multigrid schemes for the acceleration of FVM radiative heat transfer computations

ABSTRACT The development and comparison of different parallel spatial/angular agglomeration multigrid schemes to accelerate the finite volume method, for the prediction of radiative heat transfer, are reported in this study. The proposed multigrid methodologies are based on the solution of radiative transfer equation with the full approximation scheme coupled with the full multigrid method, considering different types of sequentially coarser spatial and angular resolutions as well as different V-cycle types. The encountered numerical tests, involving highly scattering media and reflecting boundaries, reveal the superiority of the nested scheme along with the V(2,0)-cycle-type strategy, while they highlight the significant contribution of the angular extension of the multigrid technique.

USING IMPROVED RADIAL BASIS FUNCTIONS METHODS FOR FLUID-STRUCTURE COUPLING AND MESH DEFORMATION

In this work the development of a partitioned FSI coupling procedure is reported, aiming to facilitate interaction between an open-source CSD (Computational Structural Dynamics) and an in-house academic CFD (Computational Fluid Dynamics) code. Attention is mainly directed towards the efficient and accurate transfer of predicted displacements, velocities (by CSD) and loads (by CFD). More precisely, spatial coupling is achieved using Radial Basis Functions (RBFs) interpolation, which enables point-based interaction, needing therefore no information for connectivities and, consequently, allowing for the utilization of different type or even intersecting structural and flow grids. Although RBFs method seems to be particularly attractive for both data transfer and mesh deformation, it suffers from a significant drawback; it calls for relatively excessive memory and computation time requirements (in its initial formulation). In case of data transfer the Partition of Unity (PoU) approach is adopted as a remedy of the aforementioned deficiency, which regards the decomposition of the examined problem into several smaller ones, to be solved independently and hence more efficiently. In mesh deformation though, improvement of computational performance is succeeded with a surface point reduction technique, based on the agglomeration of the adjacent boundary nodes, i.e., on the fusion of the RBFs centers. Despite the notable reduction of RBFs base points, the proposed method preserves sufficiently the quality of the initial grid. The proposed algorithm is evaluated against a benchmark (for FSI solvers) test case, considering the analysis of the wind action over a standard tall building model. The obtained numerical results confirm its potential for such simulations, highlighting additionally the radically improved computational performance of data transfer and grid deformation procedures.

COMPARISON OF DIFFERENT SPATIAL/ANGULAR AGGLOMERATION MULTIGRID SCHEMES FOR RADIATIVE HEAT TRANSFER COMPUTATIONS

During the past decade the 3D unstructured grids have become an important tool for radiative heat transfer simulations, extending their applications to even more complex enclosures. Nevertheless, the corresponding solvers appear to be inferior in terms of efficiency, compared to those for structured meshes. One remedy to this shortcoming appears to be the agglomeration multigrid method, based on the solution of the numerical problem on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of their neighbouring control volumes and control angles respectively. Considering this state, the enhancement of an in-house academic solver with different spatial/angular agglomeration multigrid schemes to accelerate the finite-volume method for the prediction of radiative heat transfer, is reported in this study. The incorporated multigrid methods are based on the relaxation of radiative transfer equation with the FAS approach, considering though different types of sequentially coarser spatial and angular resolutions, as well as different V-cycle types. More specifically, a nested, a uniform and an alternate scheme were developed, while they were examined in conjunction with the V(1,0), V(1,1), V(2,0) and V(2,1) V-cycles types. To further accelerate the numerical solution, a combined FMG-FAS strategy was included, according to which the whole procedure begins from the coarsest discretization (spatial and angular) and as the number of iterations is increased the FAS extends to the finer resolutions, up to the initial finest one. The proposed numerical schemes were validated against a benchmark test case, considering radiative heat transfer through a strongly scattering medium in a cubic enclosure with highly reflecting surfaces. The obtained results reveal the superiority of the nested scheme along with the V(2,0)-cycle type strategy, while they highlight the significant contribution of the angular extension of the multigrid technique.

NUMERICAL ANALYSIS OF RAREFIED GAS FLOWS USING THE ACADEMIC CFD CODE GALATEA

During the last decades considerable efforts have been exerted for the development of micro air vehicles as well as microelectromechanical systems in general, for a wide range of applications. However, such systems involve microscale rarefied gas flows, which appear to be significantly different comparing to flows at macroscale and continuum regime; it is this the reason the Navier-Stokes equations fail to simulate such phenomena without further modification. To this end, the enhancement of the in-house academic Computational Fluid Dynamics solver Galatea to encounter such simulations is reported in this study. In case of rarefied gas flows and particularly for fluids in slip flow regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip conditions as well as temperature jump ones have to be included instead. Furthermore, to increase accuracy at the same region the second-order accurate spatial slip model of Beskok and Karniadakis has been incorporated, which avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered. Due to oscillations that might appear, especially during the initial steps of the iterative procedure, a normalization scheme is additionally employed, to allow for the gradual increase of the corresponding slip/jump values. Galatea has been validated against a benchmark test case concerning rarefied laminar flow (inside the slip flow regime) over a wing with a NACA0012 airfoil in different angles of attack. The obtained results were compared with those of a reference solver, and with those obtained with the paralleld open-source kernel SPARTA, based on the Direct Simulation Monte-Carlo method. According to this last approach, the flow domain is divided into a finite number of computational cells, while the required sample macroscopic flow properties are retrieved assuming intermolecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by Galatea and SPARTA as well.

Assessment of the Academic CFD Code Galatea-I With the DARPA SUBOFF Test Case

In this study an academic CFD code, named Galatea-I, is presented, capable for simulating inviscid, viscous laminar and viscous turbulent incompressible fluid flows. It employs the RANS (Reynolds-Averaged Navier-Stokes) approach along with the SST (Shear Stress Transport) turbulence model to predict turbulent flow phenomena, such as recirculations and separations of flow, on three-dimensional unstructured hybrid grids, composed of prismatic, tetrahedral and pyramidal elements. Discretization of the governing equations is obtained with a node-centered finite-volume scheme. Parallel processing and agglomeration multigrid scheme are implemented for the acceleration of the numerical process. As the title of this paper reveals, the solver is validated against the test cases of the DARPA SUBOFF program; in particular, flows over the SUBOFF bare hull submarine geometry at two incident angles and the SUBOFF hull with fairwater configuration are examined. The obtained results, compared to available in open literature experimental data as well as results computed by reference solvers, indicate the proposed methodology’s potential to accurately simulate complex fluid flows.Copyright