Results 1 - 10 of 19

Non-oscillatory central differencing for hyperbolic conservation laws

by Haim Nessyahu, Eitan Tadmor - J. COMPUT. PHYS , 1990
"... Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in orde ..."
Abstract - Cited by 298 (25 self) - Add to MetaCart
Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required

Computing interface Motion in Compressible Gas Dynamics

by W. Mulder, S. Osher, James A. Sethian , 1992
"... A “Hamilton-Jacobi” level set formulation of the equations of motion for propagating interfaces has been introduced recently by Osher and Sethian. This formulation allows fronts to self-intersect, develop singularities, and change topology. The numerical algorithms based on this approach handle topo ..."
Abstract - Cited by 102 (14 self) - Add to MetaCart
both conservative and non-conservative differencing of the level set function and compare the two approaches. To

Third Order Nonoscillatory Central Scheme For Hyperbolic Conservation Laws

by Xu-dong Liu
"... . A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: #1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and #2. A central differencing ..."
Abstract - Cited by 69 (12 self) - Add to MetaCart
. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: #1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and #2. A central differencing

Simplified Discretization of Systems of Hyperbolic Conservation Laws Containing Advection Equations

by Ronald Fedkiw , Barry Merriman, Stanley Osher , 1999
"... The high speed flow of complex materials can often be modeled by the compressible Euler Equations coupled to (possibly many) additional advection equations. Traditionally, good computational results have been obtained by writing these systems in fully conservative form and applying the general metho ..."
Abstract - Cited by 16 (6 self) - Add to MetaCart
methodology of shock-capturing schemes for systems of hyperbolic conservation laws. In this paper, we show how to obtain the benefits of these schemes without the usual complexity of full characteristic decomposition or the restrictions imposed by fully conservative differencing. Instead, under certain

The penultimate scheme for systems of conservation laws: finite-difference ENO with Marquina’s flux splitting

by Ronald P. Fedkiw, Barry Merriman, Rosa Donat, Stanley Osher , 1998
"... This paper provides a users’ guide to a new, general finite difference method for the numerical solution of systems of convection dominated conservation laws. We include both extensive motivation for the method design, as well as a detailed formulation suitable for direct implementation. Essentially ..."
Abstract - Cited by 27 (16 self) - Add to MetaCart
. Essentially Non-Oscillatory (ENO) methods are a class of high accuracy, shock capturing numerical methods for hyperbolic systems of conservation laws, based on upwind biased differencing in local characteristic fields. The earliest ENO methods used control volume discretizations, but subsequent work [12] has

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

by Jahrul Alam, John C. Bowman
"... Abstract. A numerical model for electro-osmotic flow is described. The advecting velocity field is com-puted by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences ar ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
are second-order accurate and centered in space; however, the traditional second-order compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have de-signed a non-compact finite differencing for the Laplacian in the pressure

UNSTEADY IRROTATIONAL TRANSONIC FLOW ABOUT AIRFOILS

by R. Chipman, A. Jameson, Richard Chipman, Antony Jameson
"... Numerical difference schemes are presented for the computation of unsteady transonic flows about airfoils. A first-order system of equations in conservation form is developed for irrotational (full potential) flow and solved by finite difference methods. To enable the boundary conditions to be impos ..."
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to be imposed directly on the airfoil surface, a time-varying sheared-rectilinear coordinate transformation is used. Explicit differencing schemes are used to solve both lifting and non-lifting cases. Additionally, an alternating direction implicit (ADI) scheme has been coded for efficient solutions in the non

c © Uma Publicação da Sociedade Brasileira de Matemática Aplicada e Computacional. Implementing Implicit Schemes in GENSMAC

by C. M. Oishi, V. G. Ferreira, J. A. Cuminato, A. Castelo, M. F. Tomé
"... Abstract. Implicit schemes are studied with the purpose of introducing them in the two-dimensional GENSMAC method, for the numerical solution of unsteady new-tonian incompressible flows. By using the fractional-step approach, the Freeflow2D simulation system is employed to solve the conservation equ ..."
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equations. The viscous terms in the Navier-Stokes equations are implicitly treated via the Implicit Back-ward (IR), Crank-Nicolson (CN) and Adams-Bashforth/Crank-Nicolson (AB/CN) schemes. The convective terms are explicitly treated by the upwind differencing Variable Order Non-Oscillatory Scheme (VONOS

Theoretical and Computational Fluid Dynamics Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

by Jahrul Alam, John C. Bowman , 2002
"... Abstract. A numerical model for electro-osmotic flow is described. The advecting velocity field is com-puted by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences ar ..."
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are second-order accurate and centered in space; however, the traditional second-order compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a non-compact finite differencing for the Laplacian in the pressure

Cosmological hydrodynamics with multi-species chemistry and nonequilibrium ionization and cooling

by Peter Anninos, Yu Zhang, Tom Abel, Michael L. Norman - New. A , 1997
"... We have developed a method of solving for multi-species chemical reaction flows in non–equilibrium and self–consistently with the hydrodynamic equations in an expanding FLRW universe. The method is based on a backward differencing scheme for the required stability when solving stiff sets of equation ..."
Abstract - Cited by 9 (5 self) - Add to MetaCart
We have developed a method of solving for multi-species chemical reaction flows in non–equilibrium and self–consistently with the hydrodynamic equations in an expanding FLRW universe. The method is based on a backward differencing scheme for the required stability when solving stiff sets
Results 1 - 10 of 19