scholarly journals Data assimilation in 2D viscous Burgers equation using a stabilized explicit finite difference scheme run backward in time

2021 ◽  
pp. 1-15
Author(s):  
Alfred S. Carasso
Keyword(s):  
Finite Difference ◽  
Data Assimilation ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Burgers Equation ◽  
Explicit Finite Difference

scholarly journals A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

Dynamic Analysis of a Valve Spring With a Coulomb-Friction Damper

1990 ◽  
Vol 112 (4) ◽  
pp. 509-513 ◽  
Author(s):  
R. S. Paranjpe
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Coulomb Friction ◽  
Distributed Parameter ◽  
Friction Damper ◽  
Equivalent Viscous Damping ◽  
Valve Spring ◽  
Coulomb Damping ◽  
Explicit Finite Difference

The dynamic behavior of a distributed parameter valve spring with Coulomb damping has been modeled. Such a spring is described by a nonlinear, nonhomogeneous wave equation. This equation is solved using an explicit finite difference scheme. Some sample results are presented. The results of the finite difference scheme are compared with the results of an analytical solution for zero damping. The two compare very well. The spring is also modeled using an equivalent viscous damping coefficient. The results of this analysis are compared with those of the Coulomb damping analysis.

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