Unstructured Cartesian Grid Research Articles

Flow simulations in arbitrarily complex cardiovascular anatomies – An unstructured Cartesian grid approach

Image guided computational fluid dynamics is attracting increasing attention as a tool for refining in vivo flow measurements or predicting the outcome of different surgical scenarios. Sharp interface Cartesian/Immersed-Boundary methods constitute an attractive option for handling complex in vivo geometries but their capability to carry out fine-mesh simulations in the branching, multi-vessel configurations typically encountered in cardiovascular anatomies or pulmonary airways has yet to be demonstrated. A major computational challenge stems from the fact that when such a complex geometry is immersed in a rectangular Cartesian box the excessively large number of grid nodes in the exterior of the flow domain imposes an unnecessary burden on both memory and computational overhead of the Cartesian solver without enhancing the numerical resolution in the region of interest. For many anatomies, this added burden could be large enough to render comprehensive mesh refinement studies impossible. To remedy this situation, we recast the original structured Cartesian formulation of Gilmanov and Sotiropoulos [Gilmanov A, Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J Comput Phys 2005;207(2):457–92] into an unstructured Cartesian grid layout. This simple yet powerful approach retains the simplicity and computational efficiency of a Cartesian grid solver, while drastically reducing its memory footprint. The method is applied to carry out systematic mesh refinement studies for several internal flow problems ranging in complexity from flow in a 90° pipe bend to flow in an actual, patient-specific anatomy reconstructed from magnetic resonance images. Finally, we tackle the challenging clinical scenario of a single-ventricle patient with severe arterio-venous malformations, seeking to provide a fluid dynamics prospective on a clinical problem and suggestions for procedure improvements. Results from these simulations demonstrate very complex cardiovascular flow dynamics and underscore the need for high-resolution simulations prior to drawing any clinical recommendations.

Flow Calculation of Moving Body on Cartesian Grid by Using New Cell-Merging Method.

Flow simulation around a moving body is a challenging problem, especially when there is more than one body moving relative to each other. To tackle this problem, a Cartesian grid is used in this paper, where its non-body-fitted property allows the grid to stay stationary while the bodies move across it. As a result, it requires only local grid modification in the vicinity of body surface, which may lead to a significant saving of computational cost. On the other hand, the body-fitted grids such as structured and tetrahedral-based unstructured grids move with the body; thus global grid modification is necessary during the movement. In the present study we devised a new implementation procedure for an existing two-dimensional cell-merging method to overcome the problem of conservation regarding gas dynamic properties, a problem caused by body movement across a grid. The present method may have a better potential for extension to 3D. It is based on our previous algorithm developed for a 3D unstructured Cartesian grid and was successfully applied to several test cases in this study. In particular, the efficiency of the method is greatly improved by employing a tree-based data structure to reduce the time to find body panels during computation of the cell’s geometrical properties.

Io's plasma environment during the Galileo flyby: Global three‐dimensional MHD modeling with adaptive mesh refinement

The first results for applying a three‐dimensional multiscale ideal MHD model for the mass‐loaded flow of Jupiter's corotating magnetospheric plasma past Io are presented. The model is able to consider simultaneously physically realistic conditions for ion mass loading, ion‐neutral drag, and intrinsic magnetic field in a full global calculation without imposing artificial dissipation. Io is modeled with an extended neutral atmosphere which loads the corotating plasma torus flow with mass, momentum, and energy. The governing equations are solved using adaptive mesh refinement on an unstructured Cartesian grid using an upwind scheme for MHD. For the work described in this paper we explored a range of models without an intrinsic magnetic field for Io. We compare our results with particle and field measurements made during the December 7, 1995, flyby of Io, as published by the Galileo Orbiter experiment teams. For two extreme cases of lower boundary conditions at Io, our model can quantitatively explain the variation of density along the spacecraft trajectory and can reproduce the general appearance of the variations of magnetic field and ion pressure and temperature. The net fresh ion mass‐loading rates are in the range of ∼300–650 kg s−1, and equivalent charge exchange mass‐loading rates are in the range ∼540–1150 kg s−1 in the vicinity of Io.

MHD SIMULATION OF COMETS: THE PLASMA ENVIRONMENT OF COMET HALE-BOPP

MHD simulation results of the interaction of the expanding atmosphere of comet Hale-Bopp with the magnetized solar wind are presented. At the upstream boundary a supersonic and superalfvénic solar wind enters into the simulation box 25 million km upstream of the nucleus. The solar wind is continuously mass loaded with cometary ions originating from the nucleus. The effects of photoionization, recombination and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our MUSCL-type upwind numerical technique, MAUS-MHD (Multiscale Adaptive Upwind Scheme for MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. Detailed simulation results for the plasma environment of comet Hale-Bopp for slow and fast solar wind conditions are presented. We also calculate synthetic H2O+, CO+ and soft x-ray images for observing conditions on April 11, 1997.

Three‐dimensional multiscale MHD model of cometary plasma environments

First results of a three‐dimensional multiscale MHD model of the interaction of an expanding cometary atmosphere with the magnetized solar wind are presented. The model starts with a supersonic and super‐Alfvènic solar wind far upstream of the comet (25 Gm upstream of the nucleus) with arbitrary interplanetary magnetic field orientation. The solar wind is continuously mass loaded with cometary ions originating from a 10‐km size nucleus. The effects of photoionization, electron impact ionization, recombination, and ion‐neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our new multiscale upwind scalar conservation laws‐type numerical technique (MUSCL). We have named this the multiscale adaptive upwind scheme for MHD (MAUS‐MHD). The combination of the adaptive refinement with the MUSCL‐scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. The main findings are the following: (1) Mass loading decelerates the solar wind flow upstream of the weak cometary shock wave (M ≈ 2, MA ≈ 2), which forms at a subsolar standoff distance of about 0.35 Gm. (2) A cometary plasma cavity is formed at around 3 × 103 km from the nucleus. Inside this cavity the plasma expands outward due to the frictional interaction between ions and neutrals. On the nightside this plasma cavity considerably narrows and a relatively fast and dense cometary plasma beam is ejected into the tail. (3) Inside the plasma cavity a teardrop‐shaped inner shock is formed, which is terminated by a Mach disk on the nightside. Only the region inside the inner shock is the “true” diamagnetic cavity. (4) The model predicts four distinct current systems in the inner coma: the density peak current, the cavity boundary current, the inner shock current, and finally the cross‐tail current. (5) The calculated plasma parameters (magnetic field, plasma density, speed, and temperature) are in very good agreement with published Giotto observations.

Sonic boom predictions using a solution-adaptive full-potential code

The TranAir full-potential code, which utilizes a solution-adaptive, unstructured Cartesian grid, was used to compute near-field pressure signatures of three generic geometries: (1) a cone-cylinder; (2) a low aspect ratio rectangular wing; and (3) a delta-wing/body. Pressure signatures computed by TranAir are extrapolated to near- and midfield distances using a quasilinear extrapolation technique. Results are compared with wind-tunnel data and, where possible, with extrapolated wind-tunnel data and Whitham-method results. In general, extrapolated TranAir data is in good agreement with experimental and Whitham-method pressure signatures, but peak pressures are slightly underpredicted. It is felt that data computed too close to the model caused some of the discrepancies. The flowfield grid structure was also found to be an important issue in obtaining accurate off-body data. Results were encouraging enough to proceed with the application of TranAir to conceptual configurations in support of the NASA high speed research program (HSRP).