Cartesian Mesh Simulations for the 3rd AIAA Sonic Boom Prediction Workshop
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Spurlock, Wade M.↗
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Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop
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ARMD↗
Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes
This work assesses the effectiveness of linearized implicit Euler preconditioning for multigrid solvers using an unpreconditioned, Jacobian-free Newton Krylov method to converge the linear system of equations. Multigrid convergence rates improve to approximately 0.75 across the cases tested including a Mach 2 supersonic wedge, transonic NACA 0012 airfoil, and ONERA M6 wing. While larger Krylov subspaces increase the convergence rate, they also increase the computational cost, such that 4-8 Krylov vectors often offers the fastest turnaround. Further reductions in computational cost are achieved with a sequential hybrid preconditioner that begins with the explicit multigrid solver before transitioning to the preconditioned algorithm later on. In addition, a novel implementation of dual time stepping is extended to include both common BDF methods as well as high-order implicit Runge-Kutta schemes. This particular formulation, which uses A −1 preconditioning, is amenable to matrix-free solvers, and the L-stable methods are especially suited for meshes with arbitrarily small cut-cells. Asymptotic order of convergence is demonstrated for BDF1, BDF2, SDIRK2, and 3rd-order Radau IIA time integration with unsteady 2D vortex simulations.
ARMD↗
Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes
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ARMD↗
Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes
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TTT↗
Wall-Modeled LES of a Swept Wing with Leading-Edge Ice Using LAVA Curvilinear, Unstructured, and Cartesian Solvers
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TTT↗
Two dimensional vernier
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
Juday, Richard D.↗
Dual redundant arm system operational quality measures and their applications - Dynamic measures
Dual-arm dynamic operation quality measures are presented which quantify the efficiency and capability of generating Cartesian accelerations by two cooperative arms based on the analysis of dual-arm dynamic interactions. Dual-arm dynamic manipulability is defined as the efficiency of generating Cartesian accelerations under the dynamic and kinematic interactions between individual arms and an object under manipulation. The analysis of dual-arm dynamic interactions is based on the so-called Cartesian space agent model of an arm, which represents an individual arm as a force source acting upon a point mass with the effective Cartesian space arm dynamics and an environment or an object under manipulation. The Cartesian space agent model of an arm makes it possible to derive the dynamic and kinematic constraints involved in the transport, assembly and grasping modes of dual-arm cooperation. A task-oriented operational quality measure, (TOQd) is defined by evaluating dual-arm dynamic manipulability in terms of given task requirements. TOQd is used in dual-arm joint configuration optimization. Simulation results are shown. A complete set of forward dynamic equations for a dual-arm system is derived, and dual-arm dynamic operational quality measures for various modes of dual-arm cooperation allowing sliding contacts are established.
Lee, Sukhan↗
Toward Immersed Boundary Simulation of High Reynolds Number Flows
In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.
Kalitzin, Georgi↗
Mapping From an Instrumented Glove to a Robot Hand
An algorithm has been developed to solve the problem of mapping from (1) a glove instrumented with joint-angle sensors to (2) an anthropomorphic robot hand. Such a mapping is needed to generate control signals to make the robot hand mimic the configuration of the hand of a human attempting to control the robot. The mapping problem is complicated by uncertainties in sensor locations caused by variations in sizes and shapes of hands and variations in the fit of the glove. The present mapping algorithm is robust in the face of these uncertainties, largely because it includes a calibration sub-algorithm that inherently adapts the mapping to the specific hand and glove, without need for measuring the hand and without regard for goodness of fit. The algorithm utilizes a forward-kinematics model of the glove derived from documentation provided by the manufacturer of the glove. In this case, forward-kinematics model signifies a mathematical model of the glove fingertip positions as functions of the sensor readings. More specifically, given the sensor readings, the forward-kinematics model calculates the glove fingertip positions in a Cartesian reference frame nominally attached to the palm. The algorithm also utilizes an inverse-kinematics model of the robot hand. In this case, inverse-kinematics model signifies a mathematical model of the robot finger-joint angles as functions of the robot fingertip positions. Again, more specifically, the inverse-kinematics model calculates the finger-joint commands needed to place the fingertips at specified positions in a Cartesian reference frame that is attached to the palm of the robot hand and that nominally corresponds to the Cartesian reference frame attached to the palm of the glove. Initially, because of the aforementioned uncertainties, the glove fingertip positions calculated by the forwardkinematics model in the glove Cartesian reference frame cannot be expected to match the robot fingertip positions in the robot-hand Cartesian reference frame. A calibration must be performed to make the glove and robot-hand fingertip positions correspond more precisely. The calibration procedure involves a few simple hand poses designed to provide well-defined fingertip positions. One of the poses is a fist. In each of the other poses, a finger touches the thumb. The calibration subalgorithm uses the sensor readings from these poses to modify the kinematical models to make the two sets of fingertip positions agree more closely.
Goza, Michael↗
A climatically-derived global soil moisture data set for use in the GLAS atmospheric circulation model seasonal cycle experiment
Algorithms for point interpolation and contouring on the surface of the sphere and in Cartesian two-space are developed from Shepard's (1968) well-known, local search method. These mapping procedures then are used to investigate the errors which appear on small-scale climate maps as a result of the all-too-common practice of of interpolating, from irregularly spaced data points to the nodes of a regular lattice, and contouring Cartesian two-space. Using mean annual air temperatures field over the western half of the northern hemisphere is estimated both on the sphere, assumed to be correct, and in Cartesian two-space. When the spherically- and Cartesian-approximted air temperature fields are mapped and compared, the magnitudes (as large as 5 C to 10 C) and distribution of the errors associated with the latter approach become apparent.
Willmott, C. J.↗
Development of advanced control schemes for telerobot manipulators
To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.
Nguyen, Charles C.↗
An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies
In this paper we describe an approach for dealing with arbitrary complex, two dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.
Quirk, James J.↗
Fourier analysis of numerical algorithms for the Maxwell equations
The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.
Liu, Yen↗
Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion
Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.
Leffell, Joshua Isaac↗
A Wall-Modeled LES Perspective for the High Lift Common Research Model Using LAVA
A new immersed boundary Wall-Modelled Large Eddy Simulation (WMLES) formulation is developed to study high-lift aerodynamics on the NASA High-Lift Common Research Model (HL-CRM). A sequence of Cartesian Octree grids with sizes ranging from 100 Million through 2.02 Billion grid points is utilized to systematically assess grid-sensitivity and convergence for the in-tunnel (QinetiQ) configuration of the model, and remarkable agreement between the immersed boundary and the curvilinear body-aligned WMLES formulations is reported on grids with comparable resolutions. In the free-air configuration of the model, consistent predictions between the Curvilinear Overset and the Cartesian Octree formulations are reported for angles of attack up to C(L,max) at a=19.57. However, some differences in the onset of stall are seen between the two methods for a>20°: while the curvilinear WMLES experiences wing-root separation with increasing angle of attack (Topology A), the Cartesian Octree formulation shows a different flow topology characterized by boundary layer weakness on the main element, emanating from the pylon-wing attachment (Topology B). In order to obtain further insight into the two-distinct topologies, carefully designed numerical experiments to isolate effects of the model standoff and the tunnel wall-boundary layers are conducted using the immersed boundary WMLES formulation. The increased incidence angle-of-attack on the inboard portion of the wing due to the standoff is shown to be sufficient for triggering a switch from Topology B to Topology A in Cartesian WMLES. The role of the floor boundary layer is further examined in detail by identification of additional corner-flow vorticity generated by the viscous juncture flow interactions between the floor boundary layer and the standoff leading to formation of a strong coherent and persistent vortex on the belly-side of the fuselage. The intensity of this vortex is shown to increase with the thickness of the floor boundary layer. A further increase in the incidence angle of attack near the leading-edge strake caused by the presence of this belly-side vortex is quantified for two-distinct floor boundary layers. Both of the floor boundary layers considered result in the onset of large scale wing-root separation at a=21.47in non-confined (free-air) configurations.
TTT↗
Entity—Hardware-agnostic Particle-in-cell Code for Plasma Astrophysics. I. Curvilinear Special Relativistic Module
Entity is a new-generation, fully open-source particle-in-cell (PIC) code developed to overcome key limitations in astrophysical plasma modeling, particularly the extreme separation of scales and the performance challenges associated with evolving, GPU-centric computing infrastructures. It achieves hardware-agnostic performance portability across various GPU and CPU architectures using the Kokkos library. Crucially, Entity maintains a high standard for usability, clarity, and customizability, offering a robust and easy-to-use framework for developing new algorithms and grid geometries, which allows extensive control without requiring edits to the core source code. This paper details the core general-coordinate special relativistic module. Entity is the first PIC code designed to solve the Vlasov–Maxwell system in general coordinates, enabling a coordinate-agnostic framework that provides the foundational structure for straightforward extension to arbitrary coordinate geometries. The core methodology achieves numerical stability by solving particle equations of motion in the global orthonormal Cartesian basis, despite using generalized coordinates like Cartesian, axisymmetric spherical, and quasi-spherical grids. Charge conservation is ensured via a specialized current deposition technique using conformal currents. The code exhibits robust scalability and performance portability on major GPU platforms (AMD MI250X, NVIDIA A100, and Intel Max Series), with the 3D particle pusher and the current deposition operating efficiently at about 2 ns per particle per time step. Functionality is validated through a comprehensive suite of standard Cartesian plasma tests and the accurate modeling of relativistic magnetospheres in curvilinear axisymmetric geometries.
Hakobyan, Hayk [Flatiron Institute, New York, NY (↗