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Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…

Fluid Dynamics · Physics 2024-06-14 Hilary Weller , Christian Kuehnlein , Piotr K. Smolarkiewicz

We present an approach called guaranteed block autoencoder that leverages Tensor Correlations (GBATC) for reducing the spatiotemporal data generated by computational fluid dynamics (CFD) and other scientific applications. It uses a…

Machine Learning · Computer Science 2024-04-30 Jaemoon Lee , Ki Sung Jung , Qian Gong , Xiao Li , Scott Klasky , Jacqueline Chen , Anand Rangarajan , Sanjay Ranka

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows. The finite volume method (FVM) is an important one. In FVM, space is discretized to many grid cells. When the number of grid…

We introduce a novel data-driven method to mitigate the risk of cascading failures in delayed discrete-time Linear Time-Invariant (LTI) systems. Our approach involves formulating a distributionally robust finite-horizon optimal control…

Optimization and Control · Mathematics 2023-10-19 Guangyi Liu , Arash Amini , Vivek Pandey , Nader Motee

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

Dynamic quantum circuits integrate unitary evolution with mid-circuit measurement and feedforward, enabling conditional operations essential for efficient quantum algorithms and foundational for fault-tolerant quantum computation. However,…

Quantum Physics · Physics 2026-04-22 Christopher Tong , Liran Shirizly , Edward H. Chen , Derek S. Wang , Bibek Pokharel

Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of partial differential equations (PDE). Allowing users to…

Numerical Analysis · Mathematics 2025-02-20 Robert C. Kirby , Scott P. MacLachlan

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity…

Computational Physics · Physics 2019-10-18 Han Bao , Jinyong Feng , Nam Dinh , Hongbin Zhang

Recently, H(div)-conforming DG type methods coupled with Runge-Kutta (RK) time stepping have been widely employed for simulating high Reynolds number flows, with the convective terms treated explicitly. Although the analysis techniques of…

Numerical Analysis · Mathematics 2026-01-29 Yongbin Han , Yanren Hou , Xuehua Zhao

This study presents an automatic differentiation (AD)-based optimization framework for flow control in compressible turbulent channel flows. We developed a fully differentiable boundary condition framework that allows for the precise…

Fluid Dynamics · Physics 2025-07-01 Wenkang Wang , Xu Chu

We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK)…

Numerical Analysis · Mathematics 2018-05-28 Wensheng Tang

We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws and related systems of partial differential equations.…

Numerical Analysis · Mathematics 2025-07-09 Daniel Doehring , Hendrik Ranocha , Manuel Torrilhon

The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is…

Numerical Analysis · Mathematics 2020-11-26 Hendrik Ranocha , Mohammed Sayyari , Lisandro Dalcin , Matteo Parsani , David I. Ketcheson

This paper investigates the energy conservation properties of explicit Runge--Kutta (RK) time discretizations for autonomous skew-symmetric systems. For linear problems, we present a general framework for constructing RK methods in which…

Numerical Analysis · Mathematics 2026-05-12 Jinjie Liu , Moysey Brio

In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…

Computational Physics · Physics 2020-12-29 Zhiwei He , Yousheng Zhang , Li Li , Baolin Tian

We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of…

Numerical Analysis · Mathematics 2024-06-19 Hendrik Ranocha , Jochen Schütz

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…

Optimization and Control · Mathematics 2026-05-01 Shyam Kamal , Baby Diana , Sunidhi Pandey , Sandip Ghosh , Thach Ngoc Dinh

Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate…

Numerical Analysis · Computer Science 2014-08-19 Hong Zhang , Adrian Sandu , Paul Tranquilli

Spatiotemporal prediction is important in solving natural problems and processing video frames, especially in weather forecasting and human action recognition. Recent advances attempt to incorporate prior physical knowledge into the deep…

Computer Vision and Pattern Recognition · Computer Science 2026-02-24 Xuanle Zhao , Yue Sun , Ziyi Wang , Bo Xu , Tielin Zhang

This paper extends the Finite Elements with Switch Detection (FESD) method [Nurkanovi\'c et al., 2022] to optimal control problems with nonsmooth systems involving set-valued step functions. Logical relations and common nonsmooth functions…

Optimization and Control · Mathematics 2023-08-15 Armin Nurkanović , Jonathan Frey , Anton Pozharskiy , Moritz Diehl