Cobalt is a parallel, compressible Euler/Navier-Stokes flow solver applicable to geometries of arbitrary complexity. Its principal design features are stability, accuracy, and ease-of-use. Two- and three-dimensional unstructured grids of arbitrary cell topology are supported along with Overset grids, rigid-body motion, three equations of state, eight turbulence models, and over 20 boundary condition types. Cobalt provides detailed flow field diagnostics and direct output to major commercial post-processors.
The fundamental design philosophy of Cobalt is that it is the user who is of central importance. Not the computer. Not the software. Our goal is to dramatically simplify and streamline, from the user’s perspective, the process to obtain accurate flow simulations.
We have therefore focused on providing an Euler/Navier-Stokes solver that:
To this end, we designed a flow solver that is stable, accurate, and easy to use. Stability and accuracy promote efficiency of the user’s time, and are achieved via state-of-the-art algorithms combined with rigorous numerical testing. Ease-of-use is realized primarily with unstructured grids and minimal user input. All user input is designed to be as intuitive and easy to apply as possible. Pre-processor GUI’s, direct output to major commercial post-processors, solution diagnostics, and flow field diagnostics also facilitate the solution process.
Secondary objectives of the software design are generality and minimal solution time. Generality is achieved through unstructured grids, overset grids (an add-on module to Version 4.0), numerous boundary conditions, and multiple equations of state, to name a few. A parallel algorithm coupled with a rapidly-convergent temporal method delivers rapid solution turn-around for both steady-state and time-dependent cases.
The following presents some general details of how the above goals are accomplished.
Cobalt is fundamentally based on Godunov’s first-order accurate, cell-centered, finite volume, exact Riemann solution method[1]. Two-dimensional and three-dimensional physical spaces are discretized with unstructured grids of arbitrary cell topology. The exact Riemann solver is replaced with an inviscid flux function that alleviates the inherent shortcomings of Riemann methods, namely the ‘slowly-moving shock’ and ‘carbuncle’ problems, while retaining their inherent advantages, most notably the exact capture of stationary contact surfaces. Second-order spatial accuracy is achieved via upwind-biased reconstruction based on least-squares gradients. Stability of the second-order method is ensured by an in-house developed, multi-dimensional, TVD limiter. The inviscid flux function, reconstruction, and TVD limiter, both as a set and individually, have been constructed to minimize numerical dissipation while ensuring stability. Viscous terms, computed from the least-squares gradients, are initially formed so as to satisfy conservation and linearity-preservation. Additional machinery ensures the ‘positivity’ of the viscous terms so constructed, at the possible expense of linearity-preservation.
The above spatial operator ultimately computes residuals that an implicit temporal operator uses to advance the flow solution in time. The so-called ‘left hand side’ of the implicit method is constructed with analytical Jacobians and the resulting matrix equation is typically solved with an iterative Gauss-Seidel linear solver (an iterative Jacobi linear solver is used on vector machines). This implicit method is robust and accurate over a wide range of cases: invisicid and turbulent, unsteady and steady, from Mach = 0.005 to Mach = 20. In fact, steady-state cases are nearly always computed with a CFL of one-million. Second-order temporal accuracy and Newton sub-iterations provide accuracy with relatively large time-steps in time-dependent flows.
Three equations of state are available: ideal gas, thermally perfect gas, and equilibrium air. The thermally perfect gas equation of state assumes the gas to be calorically imperfect. To use this equation of state, the user must therefore supply a tabular listing of either Cp/R or Cp/Cv versus absolute temperature. Cobalt uses Tannehill’s [2] curve fits for the equilibrium air equation of state.
Cobalt is cast in an Arbitrary LaGrangian-Eulerian (ALE) formulation, conferring the ability to compute rigid-body motion. Rigid-body motions, in Cobalt, belong to two broad classes: ‘free’ and ‘specified’. Free motions are those where the motion of a given body is determined by the forces and moments acting upon it, such as gravity, air loads, and rotor thrust. Specified motions are those where the user specifies the motion a given body will follow. Two free motion types are available, six-degrees-of-freedom (6-DOF) and one-degree-of-freedom (1-DOF), along with three specified motion types: ‘arbitrary’ motion, ‘general’ motion, and sinusoidal-oscillation motion.
Version 4.0 of Cobalt offers an add-on Overset module, requiring separate licensing. An Overset grid-system consists of multiple overlapping grids that are treated as a single grid via a grid-assembly process. The grid-assembly process automatically determines hole-cutting, overlap regions, and interpolation weights to communicate flow field information between the separate grids. The interpolation between Overset grids is not conservative.
There are two main categories for the use of Overset grid-systems. The first models physically separate, multiple bodies with relative positions that may change in time. The second category involves overlapping surface meshes, which permits geometry modifications such as adding pods or radomes to aircraft fuselages, or modeling fins that deploy.
Currently, the Overset module in Cobalt V4.0 addresses only the positioning of physically separate, multiple bodies. The position of each body is first established by the user at the beginning of a simulation. Over the course of the ensuing solution process, the position of any given body can be held fixed, be made to follow a user-specified path, or be allowed to change subject to the forces and moments acting on the body.
Eight state-of-the-art turbulence models are available: Spalart-Allmaras, (SA) [3], SA with rotation and curvature corrections, (SARC) [4], SA with Detached Eddy Simulation (DES) [5], SARC with DES, Menter’s baseline [6], Menter’s SST, (SST) [6], SST with DES [7], and the 1998 Wilcox k-ω[8]. All turbulence models have been extensively validated.
Cobalt possesses a variety of boundary conditions to meet a wide range of flow conditions and geometry requirements. Boundary conditions are associated with, or logically linked to, boundary ‘patches’ in the grid using an easily understandable boundary condition file. Cobalt supports eight broad boundary condition classes: farfield, sink, source, solid wall, rotor/actuator, periodic, oscillatory inflow/outflow, and user-specified. There are, in general, multiple sub-types for each boundary condition class, permitting a specific boundary condition to be enforced in a particular manner. There are 23 total boundary condition sub-types, allowing a high degree of generality and flexibility in modeling flow conditions and geometries.
For parallel processing, Cobalt decomposes the single, global grid into ‘zones’ using ParMetis [9]. The number of zones is the sole input a user must supply to control the entire domain decomposition process; everything else is handled by the software. Since unstructured grids can be split into essentially equal zones, Cobalt achieves nearly perfect load balancing. In fact, Cobalt has achieved super-linear scalability on 4000 processors with cases containing roughly 6.5 million cells. This sort of scalability is available with a wide variety of machines, such as:
Grid generators that output in the Cobalt grid format include Gridgen/Pointwise, ICEM, Harpoon, and SolidMesh. Additionally, Blacksmith has converters for grids in the following formats: Gambit, Plot3D, and VGRIDns.
Cobalt outputs flow visualization files in the native formats of three leading commercial post-processors: EnSight, Fieldview, and Tecplot, eliminating the bother of converting from one format to another. Reading flow solutions directly into the post-processor reduces user time and saves memory on the user’s machine(s). A native Cobalt format is also available that, along with the Cobalt grid, can be converted for use with less commonly used post-processors. Additionally, time-dependent files can be written allowing easy visualization of unsteady data.
With problems as complex as our customers routinely tackle, responsive customer support is absolutely essential. At Cobalt Solutions, LLC, we take this responsibility very seriously. We respond to any and all requests within 24 hours - assuming we, the phones, and/or email, are alive. And because every member of Cobalt Solutions, LLC has decades of experience applying CFD to tough, real-world problems, we are very often able to quickly get you on your way again. We want you to be successful with Cobalt.
Cobalt is also very reasonably priced, offering excellent return on your investment.
Free thirty day demonstration copies are available to see if Cobalt fits the needs of your organization. If you are interested in trying out Cobalt, would like a price quote, or have other questions, please contact us.
