scholarly journals Von Neumann stability of the WONDY wavecode for thermodynamic equations of state

1977 ◽  
Author(s):  
D.L. Hicks
Keyword(s):  
Equations Of State ◽  
Von Neumann ◽  
Von Neumann Stability ◽  
Thermodynamic Equations

Stability of discrete schemes of Biot’s poroelastic equations

2020 ◽  
Author(s):  
Y Alkhimenkov ◽  
L Khakimova ◽  
Y Y Podladchikov
Keyword(s):  
Stability Analysis ◽  
Three Dimensions ◽  
Stability Conditions ◽  
Von Neumann ◽  
Explicit Schemes ◽  
Numerical Stability Analysis ◽  
Von Neumann Stability ◽  
Von Neumann Stability Analysis ◽  
Biot’S Equations ◽  
Implicit And Explicit

Summary The efficient and accurate numerical modeling of Biot’s equations of poroelasticity requires the knowledge of the exact stability conditions for a given set of input parameters. Up to now, a numerical stability analysis of the discretized elastodynamic Biot’s equations has been performed only for a few numerical schemes. We perform the von Neumann stability analysis of the discretized Biot’s equations. We use an explicit scheme for the wave propagation and different implicit and explicit schemes for Darcy’s flux. We derive the exact stability conditions for all the considered schemes. The obtained stability conditions for the discretized Biot’s equations were verified numerically in one-, two- and three-dimensions. Additionally, we present von Neumann stability analysis of the discretized linear damped wave equation considering different implicit and explicit schemes. We provide both the Matlab and symbolic Maple routines for the full reproducibility of the presented results. The routines can be used to obtain exact stability conditions for any given set of input material and numerical parameters.

scholarly journals Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. A. Banaja ◽  
H. O. Bakodah
Keyword(s):  
Wave Motion ◽  
Method Of Lines ◽  
Unconditionally Stable ◽  
Von Neumann ◽  
The Method Of Lines ◽  
Von Neumann Stability ◽  
Runge Kutta ◽  
Von Neumann Stability Analysis ◽  
Wave Phenomena ◽  
Good Agreement

The equal width (EW) equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW) equation is obtained by using the method of lines (MOL) based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing theL2andL∞error norms. The results are found in good agreement with exact solution.

Thermodynamic Derivations of Various Ammonium Salt Deposition Equations Common to the Refining Industry

CORROSION ◽  
10.5006/2855 ◽  
2018 ◽  
Vol 74 (10) ◽  
pp. 1158-1163 ◽  
Author(s):  
Brian R. Munson ◽  
Michael S. Cayard
Keyword(s):  
Ammonium Salt ◽  
Heat Exchangers ◽  
Equations Of State ◽  
Chemical Species ◽  
Refining Industry ◽  
Ammonium Salts ◽  
The Public ◽  
Salt Deposition ◽  
The Individual ◽  
Thermodynamic Equations

Ammonium salts represent a common problem for the refining industry. These saltslead to fouling of piping and heat exchangers resulting in loss of duty, underdeposit corrosionwhen wetted, and corrosive sour water solutionsonce sufficient water is available to dissociate these salts into solution. To properly manage fouling and corrosion associated with these salts, knowledge of the temperatures at which these salts will deposit is critical. In this age of process control, these temperatures can be predicted in real-time provided the salt deposition temperature relationships are known. The salt deposition equations for salts most often encountered in refining are not in the public domain. To close this gap, ammonium salt deposition equations were derived for NH4Cl, NH4HS, NH4Br, and NH4Fusing fundamental thermodynamic equations of state with published thermodynamic properties for the individual chemical species/reactions.

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

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