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At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗

DOE OSTI2020

Amesh v1.0

Amesh generates discretized grids for numerical modeling of flow and transport problems in which the formulation is based on the integral finite difference method (IFDM). For example, the output of Amesh can be used directly as input to the TOUGH2 or TOUGH3 numerical simulators. Amesh can generate 1D, 2D, or 3D numerical grids for a given set of locations, i.e., the centers of each discrete sub-domain. In the 2D areal plane Voronoi tessellation is used.

Fuller, Peter↗

DOE OSTI2021

A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation

In this report we propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Assessment of discretization schemes to reduce numerical diffusion in the calculation of complex flows

Comprehensive criteria for evaluating finite-difference schemes to reduce numerical diffusion in the solution of the Reynolds averaged Navier-Stokes equations have been established in this study. Several candidate schemes have been examined, based on these criteria. Taylor series analyses, model problem studies and examination of the difference equations have been used to assess the schemes. Two schemes, which showed the most promise, and satisfied a majority of the criteria, are recommended for incorporation into two dimensional and three dimensional computer codes for further evaluation.

Syed, S. A.↗

NASA NTRS2001

On the Definition of Surface Potentials for Finite-Difference Operators

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

Tsynkov, S. V.↗

DOE OSTI2020

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

42 ENGINEERING↗

NASA NTRS1984

A method for modeling finite-core vortices in wake-flow calculations

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.

Stremel, P. M.↗

NASA NTRS1991

A fast upwind solver for the Euler equations on three-dimensional unstructured meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a novel cell reconstruction process which results in computational times per cell comparable to those of structured codes. The approach yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicit limiting. Solutions are advanced in time by a 3-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Solutions are presented for a range of configurations in the transonic speed regime to demonstrate code accuracy, speed, and robustness. The results include an assessment of grid sensitivity and convergence acceleration by mesh sequencing.

Frink, Neal T.↗

NASA NTRS1992

Upwind scheme for solving the Euler equations on unstructured tetrahedral meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a multidimensional linear reconstruction process. The solution gradients required for the higher-order differenes are computed by a novel approach that yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicitly applying a limiter. Solutions are advanced in time by a three-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Transonic solutions are presented for two meshes around the ONERA M6 wing and demonstrate substantial accuracy and insensitivity to mesh size.

Frink, Neal T.↗

NASA NTRS2004

A Fast Upwind Solver for the Euler Equations on Three-Dimensional Unstructured Meshes

Frink, Neal T.↗

NASA NTRS1995

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗

DOE OSTI2021

Benchmarking numerical methods for impact and cratering applications

Large scale computational models are important for studying impact cratering events that are prevalent both on Earth and, more broadly, in this solar system. To address these problems, models must reliably account for both large length scales (e.g., kilometers) and relatively long time scales (hundreds of seconds). This work benchmarks two such approaches, a more traditional hydrodynamics approach and a finite-discrete element method (FDEM), for impact cratering applications. Both 2D and 3D results are discussed for two different impact velocities, 5 km/s and 20 km/s, striking normal to the target and, for 3D simulations, 45° from vertical. In addition, comparisons to previously published data are presented. Finally, differences in how these methods model damage are discussed. Ultimately, both approaches show successful modeling of several different impact scenarios.

58 GEOSCIENCES↗

NASA NTRS1984

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Kumar, A.↗

NASA NTRS1988

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Nguyen, Hung Lee↗

NASA NTRS1990

Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations

To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nondivergent and time is continuous). Among this family of schemes, there is a member that minimizes the spurious impact of infinite potential vorticities associated with infinitesimal fluid depth. The scheme is, therefore, useful for problems in which the free surface may intersect with the lower boundary.

Arakawa, Akio↗

NASA NTRS1985

Finite element algorithms for compressible flow computation on a supercomputer

Methods of applying computational fluid dynamics techniques to engineering problems are discussed. The linking factors between theoretical and applied research are the shape and weight functions which produce the Galerkin finite element schemes. The flow is unsteady, viscous, heat conducting and compressible, and steady-state flows are the asymptotic limit of unsteady flows. All flows are described by the time-averaged Navier-Stokes equations (NSE) with mass and energy conservation. Local curvilinear intrinsic coordinates are applied to discretize the NSE in arbitrary geometric domains. A modified weighted residuals approach defines the discrete analogs of the physical systems modeled and a general interpolants method is used to derive families of numerical models, both implicit and explicit, finite difference and finite elemnt, from a single point of departure. Time-dependent element approximations are achieved with a progressive assembly of generalized elements method. Hyperbolic steady-state Euler algorithms and quasi-parabolic are spatial marching algorithms for solving the discretized equations. Application of the techniques is illustrated through calculation of the compressible flow around a hypersonic flight vehicle at 100,000 ft at zero angle of attack at speeds of Mach 4-10.

Spradley, L. W.↗

NASA NTRS1988

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗

NASA NTRS1988

Discretization formulas for unstructured grids

Baumeister, Kenneth J.↗