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At least 235 records · Page 13

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DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗

NASA NTRS1990

An alternative formulation of the global sensitivity equations

To optimize the performance of any system, the sensitivity derivatives of the system's output variables with respect to its input variables must be readily available. It is also desirable that these derivatives be inexpensive to calculate as the optimization process requires many evaluations of the output variables and their derivatives. Optimization methods that have been developed for use in automated structural design programs may not be extended for use in integrated multidisciplinary design programs until adequate means of calculating accurate sensitivity derivatives of complex, internally coupled systems have been developed. Until the development of the Global Sensitivity Equations (GSE), the only method of determining the sensitivity derivatives of coupled systems has been by using finite differences. Analytical or semi-analytical derivatives do not exist as there is no analytical solution to the coupled problem. Also, difficulties arise because the finite difference method is expensive as the system has to iterate to a converged solution for each incremental input variable. The method may not be accurate, and the choice of the input variable increment may cause the difference in the output variable to be insignificant compared to computer numerical error if the choice is too small, or the process may not predict the true value of the output variable if the increment is too large. The GSE allow the system's sensitivity derivatives to be calculated as functions of the component subsystem's (local) sensitivity derivatives. These local sensitivity derivatives are calculated from specifically decoupled subsystems, whereas the GSE account for total system coupling. Since the subsystems are decoupled, it may be possible for the local derivatives to be calculated by analytical or semi-analytical methods, which generally reduce cost and improve accuracy. Several academic problems have been solved using GSE and have demonstrated encouraging results.

James, Benjamin B.↗

NASA NTRS1995

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Duque, Earl P. N.↗

NASA NTRS2001

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗

NASA NTRS2003

Divergence Free High Order Filter Methods for the Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yea, H. C.↗

NASA NTRS1974

Hypersonic chemically reacting viscous shock layers over sphere-cones and cylinder-wedges

Hypersonic, nonequilibrium viscous flow over nonanalytic blunt bodies is considered. The equations which govern the viscous shock-layer flow are presented and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with other numerical predictions as well as with experimental data. Three flow conditions are considered; the experimental, wind tunnel conditions of Pappas and Lee for a 7.5 deg sphere-cone at Mach 13 and two cases considered by Kang and Dunn, a 9 deg sphere-cone at 233,000 ft and a 20 deg sphere-cone at 280 and 310 Kft. The predictions of the present method agreed well with the experimental heat-transfer data, but substantial differences were found between the present predictions and the more approximate predictions of Kang and Dunn for heat-transfer distributions and temperature profiles.

Miner, E. W.↗

NASA NTRS1974

Viscous shock-layer flows for the space shuttle windward plane of symmetry

Predictions are presented for hypersonic, nonequilibrium viscous flows over nonanalytic blunt bodies at reentry conditions. Emphasis is placed on predictions of the viscous flowfield for the windward plane of symmetry of the space shuttle and other axisymmetric bodies which approximate the space shuttle geometry. The equations which govern the viscous shock-layer flow are presented, and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with predictions of other numerical methods as well as with experimental data.

Miner, E. W.↗

NASA NTRS1975

Hypersonic ionizing air viscous shock-layer flows over nonanalytic blunt bodies

The equations which govern the viscous shock-layer flow are presented and the method by which the equations are solved is discussed. The predictions of the present finite-difference method are compared with other numerical predictions as well as with experimental data. The principal emphasis is placed on predictions of the viscous flowfield for the windward plane of symmetry of the space shuttle orbiter and other axisymmetric bodies which approximate the shuttle orbiter geometry. Experimental data on two slender sphere-cones at hypersonic conditions are also considered. The present predictions agreed well with experimental data and with the past predictions. Substantial differences were found between present predictions and more approximate methods.

Miner, E. W.↗

NASA NTRS1979

Recent developments in finite element analysis for transonic airfoils

The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.

Hafez, M. M.↗

DOE OSTI2025

Extending TOUGH + HYDRATE with a parallel particle transport simulator: numerical investigation of sand production during gas production from hydrate deposits

A new parallel code for simulating particle transport in porous media is integrated with the TOUGH + HYDRATE simulator to investigate sand production associated with gas production from unconsolidated gas hydrate-bearing sediments (HBS). Here, the parallel coupled simulator is named THMPT and uses the integral finite difference method to describe the Darcian and non-Darcian flow of fluids and heat transport, the finite element method to describe the associated geomechanical changes, and the discrete element method to track the trajectory of individual sand particles within the HBS. The THMPT simulator is written in Fortran, incorporates multiple optimized algorithms, and can comprehensively address the coupled flow, thermal, chemical, geomechanical, and particle transport processes that characterize the system behaviors during gas production from HBS. The simulator can capture all processes involved in sand particle transport in porous media, including sand detachment, collision, clogging (i.e., bridging), and migration. A benchmark case study of sand production in the course of depressurization-induced gas production from a representative HBS reveals various distinct microscopic particle migration mechanisms and the adverse impact of sand particle detachment, transport, and clogging. The numerical investigation also examines the effect of bottomhole pressure on mitigating sand production. The simulation results indicate that sand clogging near the wellbore significantly reduces permeability, decreasing gas production by at least 50%. Lastly, the efficiency of gravel packing in mitigating sand production is numerically evaluated, revealing that the structure of the porous media appears to profoundly influence the macroscopic motion behavior of sand particles and sand clogging characteristics.

discrete element method↗

NASA NTRS1977

Computations of supersonic viscous flow over a finite-width plate

Finite difference methods were applied to solve the parabolic Navier-Stokes equations for the flow over a finite width plate at 0 deg and 10 deg angles of attack. The methods were developed on the basis of the operator factorization concept resulting in the split of a three dimensional equation into successive two dimensional equations. Backward and centered implicit factorization schemes, were used and their results were compared. Available numerical solutions and experimental data obtained at low Reynolds number conditions were also used for comparison. The backward implicit method provides a more successful solution, which ranges from the merged layer to the strong interaction regimes. Detailed structures were revealed of the shear layer around and behind the side edge.

Li, C. P.↗

NASA NTRS1991

Special class of nonlinear damping models in flexible space structures

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Hu, Anren↗

NASA NTRS1979

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Skollermo, G.↗

NASA NTRS2003

High Order Filter Methods for the Non-ideal Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yee, H. C.↗

NASA NTRS1991

Numerical identification of boundary conditions on nonlinearly radiating inverse heat conduction problems

An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.

Murio, Diego A.↗

NASA NTRS1990

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗

NASA NTRS1988

A numerical method for computing unsteady 2-D boundary layer flows

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Krainer, Andreas↗

NASA NTRS1988

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.

Lim, Joon W.↗