相关论文: Machine-precision energy conservative reduced mode…
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under-actuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear, nonhomogeneous partial differential…
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known when the initial vorticity is in $L^p$ with $1\leq p\leq…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…
Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
This paper studies the physical-constraints-preserving (PCP) Lagrangian finite volume schemes for one- and two-dimensional special relativistic hydrodynamic (RHD) equations. First, the PCP property (i.e. preserving the positivity of the…
We present a consistent high-order staggered Lagrangian hydrodynamics framework designed to reconcile an underlying disparity in existing curvilinear formulations: the mismatch between quadrature-based "strong" mass conservation and the…
This study proposes a novel spatial discretization procedure for the compressible Euler equations that guarantees entropy conservation at a discrete level for thermally perfect gases. The procedure is based on a locally conservative…
We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
We present ECHO-QGP, a numerical code for $(3+1)$-dimensional relativistic viscous hydrodynamics designed for the modeling of the space-time evolution of the matter created in high energy nuclear collisions. The code has been built on top…
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The…
Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena.…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp…
The dynamics of Quark-gluon plasma (QGP) as a lump of deconfined free quarks and gluons is elaborated. Based on the first principal we construct the Lagrangian that represents the dynamics of QGP. To induce a hydrodynamics approach, we…
A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it is firstly done that the original…