The people leading their lives near active volcanoes are under the grave threat due to the fallout of the volcanic ash. It can disrupt the air-traffic, harm the agro-based activities, destroys the residential structures due to overloading, et cetera. It is essential to understand the evolution of the fallout of the volcanic ash using attested computational methods. Eulerian models are used to simulate the deposit and transport of the volcanic ashes. Such a model uses advection-diffusion-sedimentation equation along with turbulent diffusion. Using this, allows to forecast ash loading on a surface and the ash concentration in the atmosphere.

The numerical simulations performed in the field of astronomy and astrophysics spans a broad gamut. The scope of the numerical modelling range from simulating the interior of stars, coalescing compact bodies, variable accretion flows, interstellar medium, stellar dynamics, and the formation of the Universe. The arsenal of methods (or algorithmic techniques) used to tackle such scenarios includes magnetohydrodynamics (MHD), smooth-particle hydrodynamics, N-body simulations, Monte-Carlo methods, particle-in-cell (PIC), multigrid, adaptive mesh refinement (for grid bases-simulations), et cetera. The complexity and the time involved in performing such astrophysical simulations is so high that the role of high-performance computing is indispensable.

Computational Fluid Dynamics is a discipline that deals with the numerical solution of partial differential equations (PDEs) governing the flow of fluids. The equations under consideration are the Navier-Stokes equations, describing the momentum transport in the fluid,

Rendering is used to produce a photorealistic or non-photorealistic image from a 3D model. High-level structures representing a scene are transferred into pixels accompanied by light and shading calculations of the scene’s objects. The light propagation computations are complex, expensive, and this complexity grows with the size of a scene. High performance clusters provide strong resources including processors and accelerators to speed up the process and offer a lot of memory for a large data set manipulation. Rendering is used for 3D visualization (e.g., architecture, medicine, mechanical engineering), the development of animated movies, computer games, etc.

Computational neuroscience is a branch of neuroscience which employs mathematical models, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. It employs computational simulations to validate and solve the mathematical models that - are in most cases - too complex to be solved analytically.

Density Functional Theory (DFT) is a computational quantum mechanical modelling method to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. The name Density Functional Theory comes from the use of functionals (functions that take functions as argument or return them) of the electron density.

Eigenvalue problems are a well known problem from linear algebra that can be found in many scientific fields. In structural engineering vibration analysis involves solving eigenvalue problems to obtain natural frequencies of the system. For the stability analysis of dynamical systems the sign of the eigenvalues indicate if a system will converge to a stable point or not.

Molecular Dynamics (MD) is one of the oldest applications of computers in science and up to today one of the base pillars in many computational science areas like Biology, Chemistry and Material Sciences.

Pedestrian dynamics is a field in the space of computational civil safety research. The goal is model and simulate the flow of pedestrians in emergencies. This helps to design better emergency exits in large buildings like stadiums or convention centers and plan safety concepts for mass events like concerts or demonstrations.

Seismic profiling is the technique of using sound waves to image underground rock strata, either on land or under the sea. It is widely used in oil exploration. Once the raw data has been acquired, Seismic Data Processing is then used to convert it into a meaningful form, such as a 2D picture of the cross-section being imaged, and then to enhance that image for greater clarity. This processing consists of a number of stages: filtering, deconvolution, stacking (summing separate seismic traces from the same depth) and seismic migration (the process of geometrically relocating seismic events in space or time).

Volcanic eruptions are complex phenomena that involve the dynamics of magma transfer, starting of volcanic unrest, interaction with the volcanic edifice, eruption of magma and gases, and finally the atmospheric transport of volcanic ash and aerosols. The violent activities involved in the volcanic eruption classifies it as a natural hazard. There are several hundreds of active volcanoes in our earth and millions of people risk their lives as they tend to live in the range of potential threat. The most serious concern regarding volcanic activity is its impact on air traffic, weather and pollution through the erupted volcanic gases and aerosols. One of the central issue in the volcanic eruption is the successful determination of the heights reached by the volcanic plume. It determines the effective monitoring of the volcanic ash and gases required for aviation safety, climatic studies and air quality.