scholarly journals A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation

2016 ◽  
Vol 281 ◽  
pp. 172-185 ◽  
Author(s):  
Yan Guo ◽  
Yu-feng Shi ◽  
Yi-min Li
Keyword(s):  
Finite Volume ◽  
Burgers Equation ◽  
Compact Scheme ◽  
One Dimensional ◽  
Weighted Compact Scheme ◽  
Fifth Order

scholarly journals A FINITE-VOLUME PARTICLE METHOD FOR COMPRESSIBLE FLOWS

2000 ◽  
Vol 10 (09) ◽  
pp. 1363-1382 ◽  
Author(s):  
DIETMAR HIETEL ◽  
KONRAD STEINER ◽  
JENS STRUCKMEIER
Keyword(s):  
Finite Volume ◽  
Compressible Flows ◽  
Burgers Equation ◽  
Particle Method ◽  
Finite Volume Methods ◽  
Particle Methods ◽  
One Dimensional ◽  
New Class ◽  
Shock Wave Solution ◽  
Volume Method

We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical finite-volume methods; except that the fixed spatial mesh in a finite-volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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.

Sign in / Sign up

Export Citation Format

Share Document