3.4 Development and Application of High Order Accurate Algorithms
Abstract
Major Goals: The goal of this project is to help obtaining more robust, cost effective, and reliable numerical tools for solving problems in physical applications, such as computational fluid dynamics, traffic and pedestrian flow models, cosmological turbulent flows, and optimal control. An emphasis during the proposed work period is on a study of new computational methodologies, to improve the range of applicability, efficiency, and robustness of the proposed methods for various physical problems. Attention is paid to army related applications.Accomplishments: Research has been performed and results obtained in the following directions in order to reach the major goals: Based on the recently developed fifth order WENO schemes which improve the convergence of the classical WENO schemes by removing slight post-shock oscillations, we have designed fifth order fixed-point sweeping WENO methods for efficient computation of steady state solution of hyperbolic conservation laws. A local Riemann solver for strongly nonlinear equations of state (EOS) is presented, which has suppressed successfully numerical oscillation caused by high-density ratio and high-pressure ratio across the interface between explosion products and air. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme has been developed to realize the parallel simulation of three-dimensional (3D) air explosion. The overall process of 3D air explosion of both TNT and aluminized explosives has been successfully simulated. A maximum-principle-satisfying Space-Time Conservation Element and Solution Element (CE/SE) scheme is constructed, focusing on its application to a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 27, 2018
- Accession Number
- AD1070973
Entities
People
- Chi-Wang Shu
Organizations
- Brown University