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Magnetohydrodynamic (MHD) simulations of subsonic (Mach number~$<1$) turbulence are crucial to our understanding of several processes including oceanic and atmospheric flows, the amplification of magnetic fields in the early universe,…
In this work, third-order semi-implicit schemes on staggered meshes for the shallow water and Saint-Venant-Exner systems are presented. They are based on a third-order extension of the technique introduced in Cassulli \& Cheng [1]. The…
We describe a novel splitting approach to numerical relativistic magnetohydrodynamics (RMHD) designed to expand its applicability to the domain of ultra-high magnetisation (high-$\sigma$). In this approach, the electromagnetic field is…
In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose…
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum,…
In this paper, we mainly focus on the rigorous convergence analysis of two fully decoupled, unconditionally energy-stable methods for the diffuse interface two-phase magnetohydrodynamics (MHD) model. The two methods consist of the…
Recent advancements in 3D Gaussian Splatting (3DGS) have shifted the focus toward balancing reconstruction fidelity with computational efficiency. In this work, we propose ImprovedGS+, a high-performance, low-level reinvention of the…
We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the…
In this paper, we introduce Segmentation-Driven Deformation Multi-View Stereo (SD-MVS), a method that can effectively tackle challenges in 3D reconstruction of textureless areas. We are the first to adopt the Segment Anything Model (SAM) to…
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides several high resolution, shock capturing schemes which are constructed to maintain…
We present 3DGS-LM, a new method that accelerates the reconstruction of 3D Gaussian Splatting (3DGS) by replacing its ADAM optimizer with a tailored Levenberg-Marquardt (LM). Existing methods reduce the optimization time by decreasing the…
The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods…
Due to the unique characteristics of underwater environments, accurate 3D reconstruction of underwater objects poses a challenging problem in tasks such as underwater exploration and mapping. Traditional methods that rely on multiple sensor…
We present Variable Eddington Tensor-closed Transport on Adaptive Meshes (\texttt{VETTAM}), a new algorithm to solve the equations of radiation hydrodynamics (RHD) with support for adaptive mesh refinement (AMR) in a frequency-integrated,…
Underwater pipelines are highly susceptible to corrosion, which not only shorten their service life but also pose significant safety risks. Compared with manual inspection, the intelligent real-time imaging system for underwater pipeline…
Numerical methods to improve the treatment of magnetic fields in smoothed field magnetohydrodynamics (SPMHD) are developed and tested. Chapter 2 is a review of SPMHD. In Chapter 3, a mixed hyperbolic/parabolic scheme is developed which…