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A numerical scheme has been developed to solve the quasilinear form of the transonic stream function equation. The method is applied to compute steady two-dimensional axisymmetric solar wind-type problems. A single, perfect, non-dissipative, homentropic and polytropic gas-dynamics is assumed. The four equations governing mass and momentum conservation are reduced to a single nonlinear second order partial differential equation for the stream function. Bernoulli's equation is used to obtain a nonlinear algebraic relation for the density in terms of stream function derivatives. The vorticity includes the effects of azimuthal rotation and Bernoulli's function and is determined from quantities specified on boundaries. The approach is efficient. The number of equations and independent variables has been reduced and a rapid relaxation technique developed for the transonic full potential equation is used. Second order accurate central differences are used in elliptic regions. In hyperbolic regions a dissipation term motivated by the rotated differencing scheme of Jameson is added for stability. A successive-line-overrelaxation technique also introduced by Jameson is used to solve the equations. The nonlinear equationfor the density is a double valued function of the stream function derivatives. The velocities are extrapolated from upwind points to determine the proper branch and Newton's method is used to iteratively compute the density. This allows accurate solutions with few grid points. The applications first illustrate solutins to solar wind models. The equations predict that the effects of vorticity must be confined near the surface and far away the streamlines must resemble the spherically symmetric solution. Irrotational and rotational flows show this behavior. The streamlines bend toward the rotation axis for rapidly rotating models because the coriolis force is much larger than the centrifugal force. Models of galactic winds are computed by considering the flow exterior to a surface which surrounds a uniform density oblate spheroid. Irrotational results with uniform outward mass flux show streamlines bent toward the equator and nearly spherical sonic surfaces. Rotating models for which Bernoulli's function is not constant show the sonic surface is deformed consistent with the one-dimensional theory.

While many games incorporate physics to simulate different aspects of gameplay, this is uncommon when it comes to fluid flows like wind, due to the complexity of the associated equations. The challenge increases in 3-dimensional worlds with large world maps and a real-time simulation. It is however possible to simplify a simulation by prioritizing visual and gameplay effects rather than physical accuracy, while still using a physically-sound system as a base. What this means for each game will differ depending on the architecture of the game, the desired outcome and acceptable performance costs. This paper addresses the implementation of a real-time, grid-based wind simulation in Rust for the game Veloren. A preliminary implementation with a simple graphical output was used before the simulation was integrated with the game. In Veloren, the resulting implementation is primarily server-based with a windsim system that runs the simulation itself, while the client side receives updates for the player's position, allowing the player to fly with a handglider using the wind currents created by the simulation. The performance cost of the implementation was measured for both the server and the client, using frames per second according to the grid size (space resolution) and how often the simulation is run (time resolution). When compared to the baseline before the implementation, it showed a performance cost for the server that increased with the time and space resolution. For the client side, no detectable performance cost was observed, but a lower simulation frequency resulted in sharp changes in wind direction from the player's perspective. Given that many options for optimization exist which were not systematically explored, the results show promise for the feasibility of this type of simulation in Veloren by expanding the current implementation.

Wind is a natural phenomenon that interacts with the majority of physical objects to some extent. Yet, in games this is often neglected. This is largely due to the complexity of the physics behind wind, in relation to the impact that it may have on the game experience. Adding to the complexity of wind is the fact that many modern games are networked, meaning multiple players need to share a consistent world view. Wind is inherently chaotic in nature, which is a problem for networked games that heavily favors deterministic behavior. In this thesis we will summarize the current state of the art, in games and briefly other areas. With this knowledge we push forward to improve on the existing solutions. Due to computational limitations of a real time game, we have divided up the problem into two steps. First, we run the complex computational calculations of the wind in a certain scenario in an offline setting, storing the result. Next, when running the game, we utilize the pre-computed wind scenario to let the players experience realistic wind at a low computational cost. We also investigate how to network the wind in a feasible way. The result of the project shows that doing offline computation of wind, by running physical simulations is a feasible solution for adding wind in a game setting.