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Title: Optimal Prediction of Burgers Equation


No abstract prepared.

Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE Director. Office of Science. Advanced ScientificComputing Research
OSTI Identifier:
Report Number(s):
R&D Project: 619701; BnR: KJ0101010; TRN: US200809%%341
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Multiscale modeling and Simulation; Journal Volume: 6; Journal Issue: 1; Related Information: Journal Publication Date: 2007
Country of Publication:
United States

Citation Formats

Bernstein, David. Optimal Prediction of Burgers Equation. United States: N. p., 2006. Web.
Bernstein, David. Optimal Prediction of Burgers Equation. United States.
Bernstein, David. Sun . "Optimal Prediction of Burgers Equation". United States. doi:.
title = {Optimal Prediction of Burgers Equation},
author = {Bernstein, David},
abstractNote = {No abstract prepared.},
doi = {},
journal = {Multiscale modeling and Simulation},
number = 1,
volume = 6,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
  • A new formulation of the viscous/inviscid coupling, termed X-for-mutation, has been applied to the Burgers equation: the equation is modified in such a way that the viscous terms are neglected in dependence of their magnitude. We show that the modified X-equation can be solved on a single domain at a cost comparable to the cost of solving the original equation, despite a nonlinearity being added. Furthermore, we consider a domain decomposition method, based on the X-formulation, by splitting the original problem into an inviscid Burgers equation and a X-viscous Burgers equation. The interface between the subdomains is automatically adjusted bymore » the proposed method, yielding an optimal resolution of the boundary-layer structure. 11 refs., 5 figs., 3 tabs.« less
  • A method is presented that is capable of following discontinuities in the solution of hyperbolic partial differential equations. At every time step for each cell in the neighborhood of the discontinuity, the fraction of the cell lying behind the discontinuity curve is updated. From this data the front is reconstructed. The method is applied to three scalar differential equations: inviscid Burgers' equation, the Buckley--Leverett Equation for immiscible porous flow, and the equation for two-phase miscible flow in a porous medium.
  • The note describes some numerical experiments assessing the rate of error growth when using the Random Choice Method (RCM) to compute solutions to the inviscid Burgers equation. The RCM was developed and used to study solutions of various gas dynamical systems by Chorin and his collaborators. Recently Colella has derived estimates for the error behavior of the Burgers equation. We assess the error numerically and see whether the bounds derived by Colella are achieved. Our conclusion is that the RCM does much better than expected and, indeed, approaches the best obtainable.
  • The Burgers equation is solved for Reynolds numbers [approx lt]8000 in a representation using coarse-scale scaling functions and a subset of the wavelets at finer scales of resolution. Situations are studied in which the solution develops a shocklike discontinuity. Extra wavelets are kept for several levels of higher resolution in the neighborhood of this discontinuity. Algorithms are presented for the calculation of matrix elements of first- and second-derivative operators and a useful product operation in this truncated wavelet basis. The time evolution of the system is followed using an implicit time-stepping computer code. An adaptive algorithm is presented which allowsmore » the code to follow a moving shock front in a system with periodic boundary conditions.« less