A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local dirichlet problems

2005 ◽  
Vol 102 (3) ◽  
pp. 463-495 ◽  
Author(s):  
Robert Eymard ◽  
Jürgen Fuhrmann ◽  
Klaus Gärtner
Keyword(s):  
Finite Volume ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Finite Volume Scheme ◽  
Dirichlet Problems ◽  
One Dimensional ◽  
Volume Scheme ◽  
Nonlinear Parabolic

scholarly journals On the use of a cell-centered finite-volume scheme on prismatic meshes in boundary layers

2021 ◽  
pp. 1-44
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
High Reynolds Number ◽  
Finite Volume Scheme ◽  
Wall Surface ◽  
One Dimensional ◽  
Volume Scheme ◽  
Dimensional Reconstruction ◽  
A Cell ◽  
High Reynolds

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

scholarly journals Oscillation of the solutions of systems of nonlinear parabolic equations with functional arguments

2007 ◽  
Vol 38 (4) ◽  
pp. 367-379
Author(s):  
Yutaka Shoukaku
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Differential Inequalities ◽  
Dimensional Problem ◽  
Limit Condition ◽  
Nonlinear Functional ◽  
One Dimensional ◽  
Nonlinear Parabolic ◽  
Functional Differential ◽  
Systems Of Parabolic Equations

In the present paper the oscillatory properties of the solutions of systems of parabolic equations are investigated and oscillation criteria is derived for every solution of boundary value problems to be oscillatory or satisfies some limit condition. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for nonlinear functional differential inequalities.

An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations

2019 ◽  
Vol 20 (5) ◽  
pp. 527-541
Author(s):  
M. Ghasemi
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Spatial Direction ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Nonlinear Parabolic ◽  
End Conditions ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
Diffusion Problems

AbstractTwo numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite difference discretization is used to approximate the solution at each time level. The convergence analysis is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equation with applications in fluid mechanics as well as convection–diffusion problems with applications in transport are solved to show the applicability and good performance of the procedures.

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