DYNAMIC MODE DECOMPOSITION FOR CONSTRUCTION OF REDUCED-ORDER MODELS OF HYPERBOLIC PROBLEMS WITH SHOCKS
نویسندگان
چکیده
Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity governing equations. While Lagrangian framework ROM construction resolves issue, it valid only before a shock forms. Once that occurs, characteristic lines cross each other projection from high-fidelity model space onto distorts moving grid, resulting in numerical instabilities. We address this grid distortion issue by developing physics-aware dynamic mode decomposition (DMD) method based on hodograph transformation. The latter provides map between original nonlinear system its linear counterpart, which coincides with Koopman operator. This strategy consistent spirit DMDs retains information about dynamics. Several examples are presented validate proposed DMD approach constructing accurate ROMs.
منابع مشابه
construction of vector fields with positive lyapunov exponents
in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولOn Reduced Input-Output Dynamic Mode Decomposition
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior of the data source. In this work, we consider the input-output dynamic mode decomposition method for system identification. We compare excitation approaches f...
متن کاملdiagnostic and developmental potentials of dynamic assessment for writing skill
این پایان نامه بدنبال بررسی کاربرد ارزیابی مستمر در یک محیط یادگیری زبان دوم از طریق طرح چهار سوال تحقیق زیر بود: (1) درک توانایی های فراگیران زمانیکه که از طریق برآورد عملکرد مستقل آنها امکان پذیر نباشد اما در طول جلسات ارزیابی مستمر مشخص شوند; (2) امکان تقویت توانایی های فراگیران از طریق ارزیابی مستمر; (3) سودمندی ارزیابی مستمر در هدایت آموزش فردی به سمتی که به منطقه ی تقریبی رشد افراد حساس ا...
15 صفحه اولSecond-Order Domain Decomposition Method for Three-Dimensional Hyperbolic Problems
In this paper, a non-overlapping second-order domain decomposition method for solving three-dimensional hyperbolic partial differential equation is proposed. Unconditional stability of the algorithm is analyzed. Numerical experiments show that the method is stable and very efficient. Mathematics Subject Classification: 65M06, 65M55
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of machine learning for modeling and computing
سال: 2021
ISSN: ['2689-3967', '2689-3975']
DOI: https://doi.org/10.1615/jmachlearnmodelcomput.2021036132