Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

High resolution schemes for hyperbolic conservation laws

https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=1802&context=vimsarticles

Seamless cross-scale modeling with SCHISM

A modeling paradigm is developed to augment predictive models of turbulence by effectively using limited data generated from physical experiments. The key components of the current approach involve...

/pdf/machine-learning-augmented-predictive-modeling-of-turbulent-4m92491x42.pdf

Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

In this work, a compressible Reynolds-averaged Navier-Stokes solver is used to investigate the aerodynamics of a microscale coaxial-rotor configuration in hover, to evaluate the predictive capability of the computational approach and to characterize the unsteadiness in the aerodynamic flowfield of the microscale coaxial systems. The overall performance is well-predicted for a range of rpm and rotor spacing. As the rotor spacing increases, the top-rotor thrust increases and the bottom-rotor thrust decreases, while the total thrust remains fairly constant. The thrusts approach a constant value at very large rotor spacing. Top rotor contributes about 55 % of the total thrust at smaller rotor spacing, which increases to about 58% at the largest rotor separation. The interaction between the rotor systems is seen to generate significant impulses in the instantaneous thrust and power. Unsteadiness is mainly caused due to blade loading and wake effect. Additional high-frequency unsteadiness was also seen due to shedding near the trailing edge. The phasing of the top vortex impingement upon the bottom rotor plays a significant role in the amount of unsteadiness for the bottom rotor. Interaction of the top-rotor tip vortex and inboard sheet with the bottom rotor results in a highly three-dimensional shedding on the upper surface of the blade in the outboard region and a two-dimensional shedding on the lower surface at the inboard portion of the blade. The wake of the top rotor contracts faster compared with that of the bottom rotor because of the vortex-vortex interaction. Further, the top-rotor wake convects vertically down at a faster rate due to increased inflow.

/pdf/computational-investigation-of-micro-scale-coaxial-rotor-2zu6sjh2te.pdf

Computational investigation of micro-scale coaxial rotor aerodynamics in hover

The formation and rollup of a tip vortex trailed from a hovering helicopter rotor blade is studied in detail using both computations and measurements. The compressible Reynolds-averaged Navier-Stokes equations are computationally solved on an overset mesh system. The flow measurements are made using stereoscopic particle image velocimetry. The high resolution of both the numerics and the measurements reveal multiple coherent structures in the evolving rotor tip vortex flowfield. Secondary and tertiary vortices that result from crossflow separations near the blade tip are identified. These vortices, along with a part of the trailed wake, are ultimately entrained into the tip vortex that is formed downstream of the blade's trailing edge. The simulations clearly demonstrate the resolution required to accurately represent the complex three-dimensional flowfield. The advantage of particle image velocimetry, which has the ability to make planar measurements at a given instant of time, has been fully used to validate the computational fluid dynamics predictions. Even though linear eddy viscosity models are expected to inadequately represent the details of the turbulent quantities, good agreement is seen to be achieved with the particle image velocimetry measurements of the mean flowfield. The various sources of computational and measurement uncertainties are discussed.

High-Resolution Computational and Experimental Study of Rotary-Wing Tip Vortex Formation

A high resolution computational methodology is developed for the solution of the compressible Reynolds-averaged Navier-Stokes equations. This methodology is used to study the effect of spanwise blowing as a method of tip vortex control. The numerical error is reduced by using high order accurate schemes on appropriately refined meshes. For vortex evolution problems, the equations are solved on multiple overset grids that ensure adequate resolution in an efficient manner. Reliable validation of the mean flowfield for the baseline and control configurations is obtained by adding a simple correction to the production term in the Spalart-Allmaras turbulence model. A detailed study of the underlying physics of the effects of spanwise blowing is presented.

Numerical Simulation of the Effects of Spanwise Blowing on Wing-tip Vortex Formation and Evolution

A high-resolution Reynolds-averaged Navier‐Stokes (RANS) solver is applied to study the evolution of tip vortices from rotary blades. The numerical error is reduced by using high-order accurate schemes on appropriately refined meshes. To better resolve the vortex evolution, the equations were solved on multiple overset grids that ensured adequate resolution in an efficient manner. For the RANS closure, a one equation wall-based turbulence model was used with a correction to the production term to account for the stabilizing effects of rotation in the core of the tip vortex. While experimental comparison of the computed vortex structure beyond a few chord lengths downstream of the trailing edge is lacking in the literature, reasonable validation of the vortex velocity profiles is demonstrated up to a distance of 50 chord lengths of evolution for a single-bladed rotor. For the two-bladed rotor case, the tip vortex could be tracked up to two rotor revolutions with minimal diffusion. The accuracy of the computed blade pressures and vortex trajectories confirm that the inflow distribution and blade-vortex interaction are represented correctly. The accuracy achieved in the validation studies establishes the viability of the methodology as a reliable tool that can be used to predict vortex evolution and the aerodynamic performance of hovering rotors.

High Resolution Wake Capturing Methodology for Hovering Rotors

In this work, the effect of wall interference on steady and oscillating airfoils in a subsonic wind tunnel is studied. A variety of approaches including linear theory, compressible inviscid and viscous computations, and experimental data are considered. Integral transform solutions of the linearized potential equations show an augmentation of the lift magnitude for steady flows when the wall is close to the airfoil surface. For oscillating airfoils, lift augmentation is accompanied by a significant change in the phase of the lift response. Idealized compressible Euler calculations are seen to corroborate the linear theory under conditions that are sufficiently away from acoustic resonance. Further, the theory compares well with compressible Reynolds-averaged Navier-Stokes calculations and experimental measurements over a wide range of attached flows at subsonic Mach numbers. The present methodology can thus be used to predict wall interference effects and also to help extrapolate linear and nonlinear (dynamic stall) wind tunnel data to free-air conditions.

Analysis of Wind Tunnel Wall Interference Effects on Subsonic Unsteady Airfoil Flows

The efficiency of high order accurate schemes for the solution of unsteady hyperbolic conservation laws is adversely affected by time-step restrictions that arise from monotonicity requirements. When applied to the solution of problems involving discontinuities, these restrictions render conventional high order implicit time integration schemes impractical. In the present study, a new single step second order implicit scheme that uses nonoscillatory reconstruction in space and time is presented. Both the spatial and temporal limiters are dependent on the evolving solution, and this nonlinearity allows for a circumvention of total variation diminishing bounds. Numerical results on model scalar and vector hyperbolic equations suggest that the scheme holds promise in achieving accurate and unconditionally nonoscillatory solutions.

Karthikeyan Duraisamy

Papers

High-Resolution Computational and Experimental Study of Rotary-Wing Tip Vortex Formation

Numerical Simulation of the Effects of Spanwise Blowing on Wing-tip Vortex Formation and Evolution

High Resolution Wake Capturing Methodology for Hovering Rotors

Analysis of Wind Tunnel Wall Interference Effects on Subsonic Unsteady Airfoil Flows

Implicit Scheme for Hyperbolic Conservation Laws Using Nonoscillatory Reconstruction in Space and Time