Iterated upwind schemes for gas dynamics

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness

Asymptotic-preserving projective integration schemes for kinetic equations in the diffusion limit

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on the diffusion time scale. We show that, with an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the diffusion equation, whereas the required number of inner steps does not depend on the mean free path. We also provide a consistency result. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the diffusion equation in the limit of vanishing mean free path. The analysis is illustrated with numerical results, and we present an application to the Su-Olson test

Splitting of inviscid fluxes for real gases

Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations or auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness

Universal single level implicit algorithm for gasdynamics

A single level effectively explicit implicit algorithm for gasdynamics is presented. The method meets all the requirements for unconditionally stable global iteration over flows with mixed supersonic and supersonic zones including blunt body flow and boundary layer flows with strong interaction and streamwise separation. For hyperbolic (supersonic flow) regions the method is automatically equivalent to contemporary space marching methods. For elliptic (subsonic flow) regions, rapid convergence is facilitated by alternating direction solution sweeps which bring both sets of eigenvectors and the influence of both boundaries of a coordinate line equally into play. Point by point updating of the data with local iteration on the solution procedure at each spatial step as the sweeps progress not only renders the method single level in storage but, also, improves nonlinear accuracy to accelerate convergence by an order of magnitude over related two level linearized implicit methods. The method derives robust stability from the combination of an eigenvector split upwind difference method (CSCM) with diagonally dominant ADI(DDADI) approximate factorization and computed characteristic boundary approximations

A new forward-backward sweeping parabolized Navier-Stokes algorithm with application to magnetohydrodynamic flows

A new forward-backward sweeping parabolized Navier-Stokes algorithm has been developed to efficiently compute supersonic/hypersonic flowfields with embedded separated regions. The algorithm splits the streamwise flux vector using the Steger-Warming method and employs multiple forward/backward sweeps of the flowfield in order to duplicate the results that would be obtained with the complete Navier-Stokes equations. The forward/backward sweeping of the flowfield significantly reduces the number of iterations required over previous iterative parabolized Navier-Stokes algorithms. Once a separated flow region is computed, the algorithm returns to the usual forward-space-marching mode until the next separated flow region is encountered. The new algorithm has been applied to three separated flow test cases consisting of flow over a compression ramp and two flows over a hollow-cylinder-flare geometry. The present numerical results are in excellent agreement with complete Navier-Stokes computations and experimental data. In addition, the new algorithm has been extended to efficiently compute magnetohydrodynamic (NM) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. This allows the MHD effects to be modeled by introducing source terms into the governing equations. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm with MHD effects included has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates, and 3-D supersonic viscous flows in an experimental MHD channel. The new algorithms have been successfully incorporated into NASA\u27s parabolized Navier-Stokes (UPS) code

Computation of incompressible viscous flows through turbopump components

A finite-difference, three-dimensional, incompressible Navier-Stokes formulation for calculating the flow through turbopump components is presented. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line-relaxation method. Both steady and unsteady flow calculations can be performed using the presented algorithm. In this paper, the equations are solved in steadily rotating reference frames by using the steady-state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using the Baldwin-Lomax model. Numerical results are compared with experimental measurements and good agreement is found between the two. Time-accurate calculations will be reported in future publications

Finite-volume method for industrial-scale temperature-swing adsorption simulations

We formulate a mathematical model for temperature-swing adsorption systems. A finite-volume method is derived for the numerical solution of the model equations. We specifically investigate the influence of the choice of spatial discretization scheme for the convective terms on the accuracy, convergence rate and general computational performance of the proposed method. The analysis is performed with the nonlinear Dubinin-Radushkevich isotherm representing benzene adsorption onto activated carbon, relevant for gas cleaning in biomass gasification.The large differences in accuracy and convergence between lower- and higher-order schemes for pure scalar advection are significantly reduced when using a non-linear isotherm. However, some of these differences re-emerge when simulating adsorption/desorption cycling. We show that the proposed model can be applied to industrial-scale systems at moderate spatial resolution and at an acceptable computational cost, provided that higher-order discretization is employed for the convective terms

Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed

Three-dimensional simulation of vortex breakdown

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state