In a society powered by combustion, a detailed understanding of the underlying physics is imperative.

Among the main challenges in the development of high performance, high efficiency advanced gasoline engines are end-gas, auto- or pre-ignition and super-knock, a phenomenon attributed to the formation of detonation waves.

Detonations, while wanted in few select applications, are generally to be avoided in any combustion system due to the attributed high over pressures.

Hotspots, regions of higher temperature or reactivity, play a key role in understanding both autoignition and detonation initiation.

Critical factors determining the thermomechanical response of a fluid to a local hotspot strongly depend on the hotspot size, temperature and temperature in the surrounding fluid, all of which influence different timescales of the ignition process.

As such common modeling approaches for hotspots include rapid spatially resolved energy deposition or energy deposition through boundaries, and modeling via spatially resolved thermal stratification, such as linear temperature gradients or sinusoids.

This thesis aims to improve hotspot modeling methods, by introducing a method to model a wide range of smooth temperature distributions with a small amount of parameters, and by introducing a new characterization method for the critical timescales during the initial hotspot ignition process.

First a new modeling approach is introduced in order to investigate the influence of smooth temperature variations on hotspot ignition.

Previous studies have already shown that temperature plateaus, modeling a hotspot center of finite size, can facilitate detonations in temperature gradients that otherwise wouldn't.

Realistic temperature distributions however, will have some kind of smooth, continuous temperature distribution.

A superelliptic model is introduced.

Adding only 2 additional parameters compared to the plateau and gradient model, allows this new model to parametrize smooth temperature variations across wide ranges of hotspot core sizes and gradients.

Various degrees of smoothness in the curved temperature profile can by achieved by varying a superelliptic exponent.

By using an acoustic timescale characterization approach the results obtained could be contrasted with those obtained in previous works.

It could be shown that while the intensity of the incidental pressure wave emitted at the reaction of the hotspot center is similar for plateau like and smooth temperature variations.

Smooth temperature profiles on the other hand were shown to facilitate much more severe gasdynamic responses than discontinuous temperature distributions.

It was further shown that hotspots considered partially inertially confined by means of an acoustic timescale characterization, can be extremely sensitive to slight variations in the superelliptic exponent and lead to direct detonation initiation.

Second in order to improve the predictability of the pressure response from a local reaction hotspot, a new timescale characterization approach based on critical hotspot expansion timescales is introduced and contrasted to a well investigated acoustic timescale characterization approach.

Specifically, this new approach seeks to account for the influence of the fluid surrounding a hotspot on its inertial confinement.

The new approach was shown to give a more consistent measure of whether heat release inside a hotspot or fuelpocket will occur isochorically, isobarically or in mix-fashion, and thus whether they will emit weak acoustic, strong compression or blast waves.

Over a large temperature range inside the hotspot and in surrounding fluid, hotspots with timescale ratios an order of magnitude smaller than unity would result in a pressure increase equivalent to approximately 90%+-5% of the normalized isochoric pressure increase, while timescales ratios on the order of unity would result in 50%+-10% and ratios much larger than unity around 10%+-5% of the normalized isochoric pressure increase.