Engineering topics

Lavery, John E.

Publications and source records attributed to Lavery, John E..

5 records

NASA NTRS1991

Solution of steady-state, two-dimensional conservation laws by mathematical programming

A truly two-dimensional algorithm is created for solving the steady-state two-dimensional conservation-law problem. An overdetermined system of algebraic equations is obtained through discretization by finite-volume formulas. These equations are perturbed nonsingularly and are solved by an efficient geometrically oriented l(1) procedure. The basic algorithm and the theory for the linear case f(u) = u are presented, and computational results for the nonlinear case f(u) = sq u are also analyzed. It is noted that the l(1) procedure captures boundary shocks as well as oblige and zigzag interior shocks in bands that are one cell wide, and the solution values are accurate up to the edge of the shock.

Lavery, John E.↗

NASA NTRS1990

Calculation of shocked one-dimensional flows on abruptly changing grids by mathematical programming

Cell-centered finite differences on cells of an arbitrarily spaced grid are presently used to discretize the steady-state inviscid and nearly inviscid Burgers' equations for steady-state shocked flow in a quasi-one-dimensional nozzle. The everdetermined system of nonlinear algebraic equations thus obtained is solved by a procedure which minimizes a weighted sum of the residuals' absolute values. Numerical solutions for both viscous and inviscid problems are accurate and nonoscillatory, on grids whose abrupt mesh lengths refinements are as great as a factor of 10,000.

Lavery, John E.↗

NASA NTRS1989

Numerical simulation of thermocapillary bubble migration under microgravity for large Reynolds and Marangoni numbers

A numerical procedure in which the Navier-Stokes equations are discretized using tightly coupled discretizations of pressure derivatives and continuity equations is used here to extend the range of known terminal velocities of gaseous bubbles in liquids well beyond that in previous investigations. Computations performed for Reynolds numbers up to 2000 and Marangoni numbers up to 1000 show only a modest variation of the scaled bubble velocity between 0.16 and 0.5. The bubble velocity is influenced more by the Marangoni number than by the Reynolds number.

Balasubramaniam, R.↗

NASA NTRS1989

Calculation of shocked flows by mathematical programming

A framework for using mathematical programming to solve Burgers' equation is presented. The steady-state inviscid Burgers' equation with given boundary conditions is considered, and the physically relevant solution is discretized using a four-point difference scheme for the viscous term and a two-point difference scheme for the inviscid term. The framework is then used to solve the Euler equations for quasi-one-dimensional flows on grids with variable spacing.

Lavery, John E.↗

NASA NTRS1988

Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming

In order to obtain the physically relevant discontinuous numerical solution, the steady-state inviscid Burgers' equation is singularly perturbed through the addition of a small amount of viscosity. A 'cell-centered' finite-difference scheme is proposed which employs two points for the inviscid part and four points for the viscous one. While difficulties are experienced in the capture of interior layers centered at node points, computational results for interior layers centered between node points, and for boundary layers, exhibit accurate nonoscillatory solutions whose discontinuities are captured in one cell on both coarse and fine grids.

Lavery, John E.↗