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Results for “Finite volume method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
DOE OSTI2024

Cost-efficient finite-volume high-order schemes for compressible magnetohydrodynamics

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. The algorithmic architecture of this method is very close to that of commonly employed second-order schemes: it requires only one reconstructed value per face for each computational cell, independently of the scheme's order. This property is highly beneficial for the numerical efficiency. It results from reusing the required values already available in neighboring grid cells, in contrast to standard algorithms that require a number of reconstructions and evaluations which increases with the scheme's order of accuracy. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks. Benefits of this method are shown through applications in turbulent flows.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Category 5 problem solution using an unstructured finite volume algorithm

For the simulation of flows with complex geometries, unstructured finite volume methods have proven to be very popular, and simulations of a large number of flows have been done with good results using this approach. Since most of the simulations to date were done for steady flows, it is not clear that present unstructured finite volume algorithms can accurately track the unsteady propagation of acoustic waves in a computation. Therefore, there is a need to assess the accuracy of these methods for acoustic calculations. In this paper, we perform the numerical simulation of a very small amplitude acoustic wave incident on the non-uniform steady flow in a quasi- 1 D convergent-divergent nozzle using an unstructured finite volume algorithm with piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for the steady flow by running the simulation with a sequence of successively finer meshes. Then the unsteady numerical solution with the acoustic perturbation is presented.

Bui, Trong T.↗
NASA NTRS1982

A vectorized, finite-volume, adaptive grid algorithm applied to planetary entry problems

An adaptive grid, finite-volume method has been applied to problems in planetary entry for computing complete flowfields. The adaption algorithm is implicit in nature and is keyed to resolve user specified gradients. The finite-volume algorithm is explicit, utilizing a maximum time step advancement at each grid point to accelerate convergence to the steady state. The present version of the code is for the laminar flow of a perfect gas. The role of the adaption algorithm in resolving various features of blunt body/wake flow for planetary entry conditions is emphasized.

Gnoffo, P. A.↗
NASA NTRS1986

Numerical prediction of cold turbulent flow in combustor configurations with different centerbody flame holders

A numerical study of cold turbulent flow in a combustor containing a centerbody flame holder is presented. The axisymmetric Navier-Stokes equations incorporating a k-epsilon turbulence model were solved in a nonorthogonal curvilinear coordinate system. The finite volume method, applied to a staggered grid system, was used to discretize the differential equations. These finite differenced equations were then solved iteratively utilizing the SIMPLE algorithm described by Patankar (1980). Solutions were obtained for two combustor duct geometries with various centerbody flame holders which included a disk, a cone, and a sphere. The extent of mixing due to these bodies was evaluated. A comparison with previously obtained experimental data yielded moderately good agreement.

Yung, C. N.↗
NASA NTRS2007

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Amar, Adam J.↗
NASA NTRS1993

A multiblock/multigrid Euler method to simulate 2D and 3D compressible flow

An efficient and flexible multiblock/multigrid Euler solver is described which uses a cell-centered finite-volume method based on a multigrid implementation of the alternating direction implicit algorithm. The fully conservative treatment of the inter-block boundary allows the passage of discontinuities across block boundaries with minimum distortion of the solution. Information is exchanged between blocks by using surface arrays which contain all the data needed to update the inter-block boundary conditions. The proposed multiblock/multigrid approach is considered to be feasible for solving flow problems involving complex geometries.

Wang, Lixia↗
NASA NTRS1995

Thermocapillary convection in a rectangular cavity with a deformable interface

A finite-volume method and a boundary element technique are used to compute two-dimensional (2D) thermocapillary convection in a rectangular cavity. The free surface is deformable and the deviations from a flat interface, h, are assumed small in the finite-volume calculations as appropriate for small Capillary (Ca). Two asymptotic approaches are employed; the first is an expansion valid as Ca tends towards 0 and the second assumes h tends towards 0, retaining Ca explicitly as a parameter. On the other hand, the boundary elements approach can be used with O(1) surface deformations. These three different formulations are used to calculate thermocapillary motions in fluids with small Prandtl numbers of about 0.01, Ca less than 0.05, aspect ratios (width/height) 1, 2 and 4, and various values of the Maragoni number (Ma). The same solutions are calculated with these different approaches and are found in good agreement for values of Ca up to 0.05. All solutions calculated are steady, which is both in agreement and disagreement with recently published results by different authors employing different numerical techniques.

Mundrane, M.↗
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 NTRS2012

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

We present preliminary development of an approach for simulating high Reynolds number steady compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider both laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells, and uses a wall model to address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features a forward evaluation for flow velocity and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as approx.0.1% chord. With the current analytic wall model, one or two additional refinements near the wall are required to obtain mesh converged values of skin friction.

Berger, Marsha↗
DOE OSTI2025

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗
NASA NTRS1988

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Yung, Chain Nan↗
NASA NTRS1998

Delta Clipper-Experimental In-Ground Effect on Base-Heating Environment

A quasitransient in-ground effect method is developed to study the effect of vertical landing on a launch vehicle base-heating environment. This computational methodology is based on a three-dimensional, pressure-based, viscous flow, chemically reacting, computational fluid dynamics formulation. Important in-ground base-flow physics such as the fountain-jet formation, plume growth, air entrainment, and plume afterburning are captured with the present methodology. Convective and radiative base-heat fluxes are computed for comparison with those of a flight test. The influence of the laminar Prandtl number on the convective heat flux is included in this study. A radiative direction-dependency test is conducted using both the discrete ordinate and finite volume methods. Treatment of the plume afterburning is found to be very important for accurate prediction of the base-heat fluxes. Convective and radiative base-heat fluxes predicted by the model using a finite rate chemistry option compared reasonably well with flight-test data.

Wang, Ten-See↗
DOE OSTI2025

Nonlinear simulation of under-resolved flows with shocks

Here, we consider the numerical simulation of advection-dominated flows whose wide range of physical length scales exceed the memory capacity of finite computers. Simulating flows with shocks and turbulence presented challenges for the earliest computers that were quickly overcome by the development of new numerical methodology. Principal among those new ideas were artificial viscosity and finite volume methods, concepts that remain in common use today. We begin by describing the history of those methods, the innovators and their motivations. We then describe the development of finite scale theory, a reformulation of Navier–Stokes theory that exposes the physical principles on which artificial viscosity is based. We discuss the essential properties of the finite scale equations, the observer, unresolved kinetic energy and inviscid energy dissipation. We briefly consider the implementation of the finite scale equations on the computer from the point of view of Gisin’s conjectures about finite information.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Some recent progress in transonic flow computation

Although the development of a finite difference relaxation procedure to solve the steady form of equations of motion gave birth to the study of computational transonic aerodynamics and considerable progress has been made using the small disturbance theory, no general analytical solution method yet exists for transonic flows that include three dimensional unsteady, and viscous effects. Two techniques are described which are useful in computational transonic aerodynamics applications. The finite volume method simplifies the application of boundary conditions without introducing the constriction associated with small disturbance theory. Governing equations are solved in a Cartesian coordinate system using a body-oriented and shock-oriented mesh network. Only the volume and surface normal directions of the volume elements must be known. The other method, configuration design by numerical optimization, can be used by aircraft designers to develop configurations that satisfy specific geometric performance constraints. Two examples of airfoil design by numerical optimization are presented.

Ballhaus, W. F.↗
NASA NTRS1993

A multigrid method for steady Euler equations on unstructured adaptive grids

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Riemslagh, Kris↗