Junming Duan
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View article: A fourth-order active flux method for parabolic problems with application to porous medium equation
A fourth-order active flux method for parabolic problems with application to porous medium equation Open
The active flux (AF) method is a compact high-order finite volume method originally proposed for solving hyperbolic conservation laws, in which cell averages and point values at cell interfaces are evolved simultaneously. This paper develo…
View article: An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling
An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling Open
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed he…
View article: Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term
Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term Open
The Active Flux (AF) is a compact, high-order finite volume scheme that allows more flexibility by introducing additional point value degrees of freedom at cell interfaces. This paper proposes a positivity-preserving (PP) AF scheme for sol…
View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation Open
The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value…
View article: High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes
High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes Open
This paper develops high-order accurate well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers M⩾2) shallow water equations (SWEs) with non-flat bottom topography on both fixed and adaptive mo…
View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: Two-dimensional case
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: Two-dimensional case Open
This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-preserving (BP) limitings, which is an extension of our prev…
View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: One-dimensional case
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: One-dimensional case Open
The active flux (AF) method is a compact high-order finite volume method that evolves cell averages and point values at cell interfaces independently. Within the method of lines framework, the point value can be updated based on Jacobian s…
View article: Machine-Learning-Enhanced Real-Time Aerodynamic Forces Prediction Based on Sparse Pressure Sensor Inputs
Machine-Learning-Enhanced Real-Time Aerodynamic Forces Prediction Based on Sparse Pressure Sensor Inputs Open
Accurate real-time prediction of aerodynamic forces is crucial for the navigation of unmanned aerial vehicles (UAVs). This paper presents a data-driven aerodynamic force prediction model based on a small number of pressure sensors located …
View article: High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes
High-order accurate well-balanced energy stable finite difference schemes for multi-layer shallow water equations on fixed and adaptive moving meshes Open
This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our pre…
View article: High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography
High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography Open
This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non flat bottom topography. To enable the construction of the ES schem…
View article: Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs
Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs Open
Accurate prediction of aerodynamic forces in real-time is crucial for autonomous navigation of unmanned aerial vehicles (UAVs). This paper presents a data-driven aerodynamic force prediction model based on a small number of pressure sensor…
View article: High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography
High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography Open
This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non-flat bottom topography. To enable the construction of the ES schem…
View article: Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems Open
Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…
View article: High-order accurate entropy stable adaptive moving mesh finite difference schemes for (multi-component) compressible Euler equations with the stiffened equation of state
High-order accurate entropy stable adaptive moving mesh finite difference schemes for (multi-component) compressible Euler equations with the stiffened equation of state Open
This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state. T…
View article: Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections
Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections Open
This paper derives the arbitrary order globally hyperbolic moment system for a non-linear kinetic description of the Vicsek swarming model by using the operator projection. It is built on our careful study of a family of the complicate Gra…