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A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation…
We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing…
The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While models based on this simplified geometry provide only approximations to the true processes of instability-driven mass and angular…
Cloud and precipitation microphysics packages in atmospheric general circulation models typically use first-order time integration methods with a large time step, requiring ad hoc limiters and substepping of the sedimentation scheme to…
We present the FARGO3D code, recently publicly released. It is a magnetohydrodynamics code developed with special emphasis on protoplanetary disks physics and planet-disk interactions, and parallelized with MPI. The hydrodynamics algorithms…
Radiative transfer is an important component of hydrodynamic simulations as it determines the thermal properties of a physical system. It is especially important in cases where heating and cooling regulate significant processes, such as in…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
A newly developed sensitivity-driven approach is employed to study the role of energetic particles in suppressing turbulence-inducing micro-instabilities for a set of realistic JET-like cases with NBI deuterium and ICRH $^3$He fast ions.…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain…
By analogy with the kinetic theory of gases, most turbulence modeling strate- gies rely on an eddy viscosity to model the unresolved turbulent fluctuations. How- ever, the ratio of unresolved to resolved scales - very much like a degree of…
We investigate water and deuterated water chemistry in turbulent protoplanetary disks. Chemical rate equations are solved with the diffusion term, mimicking turbulent mixing in vertical direction. Water near the midplane is transported to…
We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system,…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
Recent three-dimensional radiative hydrodynamics simulations of protoplanetary disks report disparate disk behaviors, and these differences involve the importance of convection to disk cooling, the dependence of disk cooling on metallicity,…
This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and…
Uncertain fractional differential equation (UFDE) is a kind of differential equation about uncertain process. As an significant mathematical tool to describe the evolution process of dynamic system, UFDE is better than the ordinary…
We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to show…