Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.

Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems

Abstract: We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations.We can compute branches of solutions with limit points, bifurcation points, etc.Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations.

Flow-thermal-structural study of aerodynamically heated leading edges

Abstract: A finite element approach for integrated fluid-thermal-structural analysis of aerodynamically heated leading edges is presented. The Navier-Stokes equations for high speed compressible flow, the energy equation, and the quasi-static equilibrium equations for the leading edge are solved using a single finite element approach in one integrated, vectorized computer program called LIFTS. The fluid-thermal-structural coupling is studied for Mach 6.47 flow over a 3-in diam cylinder for which the flow behavior and the aerothermal loads are calibrated by experimental data. Issues of the thermal-structural response are studied for hydrogen-cooled, super thermal conducting leading edges subjected to intense aerodynamic heating.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations

Abstract: A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain Where the resulting cells intersect bodies, polygonal 'cut' cells are created The geometry of the cut cells is computed using polygon-clipping algorithms The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells A multi-stage time-stepping scheme is used to reach a steady-state solution Validation of the Euler solver with benchmark numerical and exact solutions is presented An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations The error of the approach is directly compared to a structured solver formulation A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary A hybrid Cartesian/body-fitted grid generation approach is demonstrated In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented

Modeling shock-wave deformation via molecular dynamics

Abstract: Molecular dynamics (MD), where the equations of motion of up to thousands of interacting atoms are solved on the computer, has proven to be a powerful tool for investigating a wide variety of nonequilibrium processes from the atomistic viewpoint. Simulations of shock waves in three-dimensional (3D) solids and fluids have shown conclusively that shear-stress relaxation is achieved through atomic rearrangement. In the case of fluids, the transverse motion is viscous, and the constitutive model of Navier-Stokes hydrodynamics has been shown to be accurate---even on the time and distance scales of MD experiments. For strong shocks in solids, the plastic flow that leads to shear-stress relaxation in MD is highly localized near the shock front, involving slippage along close-packed planes. For shocks of intermediate strength, MD calculations exhibit an elastic precursor running out in front of the steady plastic wave, where slippage similar in character to that in the very strong shocks leads to shear-stress relaxation. An interesting correlation between the maximum shear stress and the Hugoniot pressure jump is observed for both 3D solid and fluid shock-wave calculations, which may have some utility in modeling applications. At low shock strengths, the MD simulations show only elastic compression, with no permanent transverse atomic strains. This result for perfect 3D crystals is also seen in calculations for 1D chains. We speculate that, if it were practical, a very large MD system containing dislocations could be expected to exhibit more realistic plastic flow for weak shock waves too.

On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe

Abstract: The bifurcation structure is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick [J. Fluid Mech. 242, 491 (1992)]. The flow considered has been restricted to a two‐dimensional parameter space comprising the Reynolds number Re and the relative swirl V0 of the incoming swirling flow. The bifurcation diagram is constructed by solving the time‐dependent axisymmetric Navier–Stokes equations. The stability of the steady results presented by Beran and Culick, obtained from a steady axisymmetric Navier–Stokes code, has been confirmed. Further, the steady solution branch has also been extended to much larger V0 values. At larger V0, a stable unsteady solution branch has been identified. This unsteady branch coexists with the previously found stable steady solution branch and originates via a turning point bifurcation. The bifurcation diagram is of the type described by Benjamin [Proc. R. Soc. London Ser. A 359, 1 (1978)] as the canonical unfolding of a pitchfork bifurcation. This type of bifurcation structure in the two‐dimensional parameter space (Re,V0), suggests the possibility of hysteresis behavior over some part of parameter space, and this is observed in the present study. The implications of this on the theoretical description of vortex breakdown and the search for a criterion for its onset are discussed.