How does buddhism describe what exactly, or where exactly, or how exactly, consciousness exists?

Maybe you could also appreciate an answer that does not come directly from Buddhism but from paraconsistent logic. This logic is not the everyday classical logic which you use in computer science (actually you could use it, though it is not widespread). Still, there are quite strong parallels between this type of logic and Buddhism. The reason I am browsing this SE and trying to learn about Buddhism is because of my interest in that logic. I can recommend books by Graham Priest, "One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness" and "The Fifth Corner of Four". First book provides explanation on how this logic can solve a number of hard problems that classical logic fails at, including how pluralities form unities (this can provides insights for aggregates and heaps part of your question) and the mind and body problem (you do not mention it explicitly, but I understood that the second paragraph in your question is about it). Last third of this book revisits some of the discussed topics from the Buddhism viewpoint. Second book is very readable account of parallels between Buddhist metaphysics and paraconsistent logic. I hope I am not making a very bad pun if I say that paraconsistent logic is a middle way between computer science and Buddhism.

Here I will give a sketch of how the problem of unity can be solved. If you use classical logic to think about how multiple things can form a unity, you run into a problem called Bradley's regress. Imagine that you are building a brick house. At first you have bricks stacked in a shape of a cube, but after the building is completed, they are stacked in the shape of a house. In the first case the bricks do not constitute a single object house, but in the second case they do. An intuitive explanation to how this comes about is that the unity of house from a plurality of bricks is accomplished by the relations between the bricks. So, you take a set of bricks and add a set of relations and you have unity. Well, this works as long as you think of relations as being a different type of objects than the bricks, as you can not explain how a bunch of objects form a unity if you just add even more objects of same kind to them. In this example it is easy think of relations different than the bricks, as bricks are physical and relations abstract objects. Also, you have to just accept that the relations do join the bricks, there is no explanation how they do it. So this is where the Bradley's regress kicks off, if you try to find the answer here, on this new level. How do bricks and relations interact? Well, you can add more relations that will explain that, but then how do these new relations interact with the old ones on one side and the bricks on the other? Furthermore, you can try to think about different examples that are more abstract, for example how words make sentences and how multiple pieces of information can be combined into an idea. Hopefully these additional examples can show that separating objects in different kinds is not always easy.

Graham Priest was able to avoid Bradley's regress by introducing a special type of object, that he named gluon. Gluon had to be inconsistent to do this, to have contradictory properties. However, you can not reason about contradictory objects in classical logic, so paraconsistent logic has to be used.

Gluon to glue together all the bricks into a unity of one house, needs to be identical to every single brick, as well as to be identical with that house. Differently said, to have same properties as all of the bricks and the house. There is no need to explain the joining of the bricks to the gluon, the gluon is already every single brick, and through being all of the bricks at the same time, all of the bricks form a unity of a house. All of this can be proven formally as well. The contradictions of the gluon should be easy to spot now. For example, there is one brick in the front wall, and when you ask if the gluon is in the front wall, the answer is both yes and no, because gluon also has the properties of a brick in the back wall, which is not in the front wall.

What is left, is to accept that the paraconsistent logic is applicable for explaining the physical world, which is not a simple task. Beside higher complexity and lesser intuitiveness compared with classical logic, it carries its own bag of problems. Of which the biggest might be how are we to accept that the contradictions are real? This is where Buddhism could come in handy and I hope better informed people can provide answers to that. I can only point towards the quantum mechanics, Schrodinger’s cat and double-slit experiment. It looks like we have measurable contradictions in physics.

I have no compartmentalized Abhidharma-type technical terms for you, but the answer to your question is mentioned quite succinctly and beautifully here:

"Herein, Bahiya, you should train yourself thus: 'In the seen will be merely what is seen; in the heard will be merely what is heard; in the sensed will be merely what is sensed; in the cognized will be merely what is cognized.' In this way you should train yourself, Bahiya.

"When, Bahiya, for you in the seen is merely what is seen... in the cognized is merely what is cognized, then, Bahiya, you will not be 'with that.' When, Bahiya, you are not 'with that,' then, Bahiya, you will not be 'in that.' When, Bahiya, you are not 'in that,' then, Bahiya, you will be neither here nor beyond nor in between the two. Just this is the end of suffering."

UD.1.10

As a computer scientist interested in the origin of the universe and the mind, I finally have found some ancient stuff of the type of substance and depth I am looking for, the Abhidhamma. The first part of the Vibhanga (one of the sections of the Abhidhamma) talks about "aggregates" or "heaps" or "groups", Skandha. This to me seems like it is near the foundation of what a computational model of consciousness would need to consider, as consciousness is one of the types of heaps or skandha.

The five aggregates are found in the Pali suttas. Regardless, Buddhism says nothing about your idea about the "origin" of consciousness. In the Pali suttas, the "origin" ("samudaya") of consciousness merely refers to when consciousness is the object of craving leading to the origin of suffering. The suttas say:

And what is the origin of form, feeling, perception, choices, and consciousness?

Ko ca, bhikkhave, rūpassa samudayo, ko vedanāya samudayo, ko saññāya samudayo, ko saṅkhārānaṃ samudayo, ko viññāṇassa samudayo?

It’s when a mendicant approves, welcomes, and keeps clinging.

Idha, bhikkhave, bhikkhu abhinandati abhivadati ajjhosāya tiṭṭhati.

SN 22.5

My question at this point in learning about this is, how exactly is consciousness structured in this model?

The above question is unrelated to Buddhism, which concerns itself with how consciousness partakes in the origination of suffering.

Where does consciousness exist exactly.

Again, the above question is unrelated to Buddhism.

As a human being, I feel my body

No. Consciousness feels the body rather than the ego.

but my conscious awareness feels like it is in the center of my brain.

Really?

I can understand and model how a consciousness can use sensory organs to perceive information

Yes, Buddhism says this.

but I don't understand how the consciousness itself can form.

Again, the above question is unrelated to Buddhism.

If everything is information in the end, or bundles of flowing information like these heaps/skandha how does it aggregate and flow in a bundle in such a way to generate consciousness which you can feel?

Again, the above question is unrelated to Buddhism.

I can even go so far as to imagine something like a biological cell with its complicated machinery going so far as to gain control over its environment, so that as a machine it is so complex and highly functional that it acts like a conscious being. This isn't too hard to imagine. But what is hard to imagine is how the consciousness is stored, or where it is! How can I perceive and feel the perception is in the center of my brain?

Again, the above question is unrelated to Buddhism.

What does skandha and the Abhidhamma have to say about this, it's structure?

Probably nothing.

“... how exactly is consciousness structured in this model?” Consciousness has no form or “structure.” It is like “ether.”

“Where does consciousness exist exactly?”

Nowhere, yet everywhere. Whether in a physical shell, or as part of the nameless void, consciousness has no barrier or confine to its existence.

“...but I don't understand how the consciousness itself can form.” Consciousness does not form. It merely exists. You confuse consciousness with the arisal of a physical or mental aggregate of consciousness and desire.

Perhaps this will help explains it a bit better: https://www.lionsroar.com/the-four-layers-of-consciousness/

The five aggregates are form, feeling (or sensation), perception, consciousness and mental formations.

These are part of name-and-form, the mentality-materiality or mind-and-body model.

Form is body. The rest are part of "name" or mind, with feeling and mental formations connecting the mind to the body.

Feeling or sensation senses from the six sense media of eyes, ears, nose, tongue, body and mind, e.g. images, sounds, smells, thoughts.

Perception matches it to previously recognized objects (e.g. images, sounds, thoughts). Memory is part of this function.

Consciousness is the mental function that focuses on and experiences the mental objects and based on this, the mind leads to the next mental processes forming thoughts, words and actions (i.e. mental formations). There are six types of consciousness related to the six sense media.

Please read the following quote and also the whole page, to get a deeper view into the concepts.

From The Abhidhamma in Practice by N.K.G. Mendis:

The Ultimate Realities

The Abhidhamma deals with realities existing in an ultimate sense, called in Pali paramattha dhammaa. There are four such realities:

1. Citta, mind or consciousness, defined as that which knows or experiences an object. > Citta occurs as distinct momentary states of consciousness.
2. Cetasikas, the mental factors that arise and occur along with the cittas.
3. Ruupa, physical phenomena, or material form.
4. Nibbaana.

Citta, the cetasikas, and ruupa are conditioned realities. They arise because of conditions and disappear when their conditions cease to sustain them. Therefore they are impermanent. Nibbaana is an unconditioned reality. It does not arise and therefore does not fall away. These four realities can be experienced regardless of what name we give them. Any other thing — be it within ourselves or without, past, present, or future, coarse or subtle, low or lofty, far or near — is a concept and not an ultimate reality.

Citta, cetasikas, and nibbaana are also called naama. The two conditioned naamas, citta and cetasikas, together with ruupa make up naama-ruupa, the psycho-physical organism. Each of us, in the ultimate sense, is a naama-ruupa, a compound of mental and material phenomena, and nothing more. Apart from these three realities that go to form the naama-ruupa compound there is no ego, self, or soul. The naama part of the compound is what experiences an object. The ruupa part does not experience anything. When the body is injured it is not the body, which is ruupa, that feels the pain, but naama, the mental side. When we are hungry it is not the stomach that feels the hunger but again the naama. However, naama cannot eat the food to ease the hunger. The naama, the mind and its factors, makes the ruupa, the body, ingest the food. Thus neither the naama nor the ruupa has any efficient power of its own. One is dependent on the other; one supports the other. Both naama and ruupa arise because of conditions and perish immediately, and this is happening every moment of our lives. By studying and experiencing these realities we will get insight into: (1) what we truly are; (2) what we find around us; (3) how and why we react to what is within and around us; and (4) what we should aspire to reach as a spiritual goal.

The Cittas

Awareness is the process of cittas experiencing objects. For a citta to arise it must have an object (aaramma.na). The object may be a color, sound, smell, taste, something tangible, or a mental object. These are the six external objects. Strictly speaking a mental object can be an internal phenomenon, such as a feeling, a thought, or an idea, but as forming the objective sphere of experience they are all classed as external. Corresponding to these external objects there are six internal sense faculties, called "doors" since they are the portals through which the objects enter the field of cognition. These are the eye, ear, nose, tongue, body and mind. Each of the five physical sense faculties can receive only its appropriate object; the mind door, however, can receive both its own proper mental objects as well as the objects of the five physical senses. When a door receives its object, there arises a corresponding state of consciousness, such as eye-consciousness, ear-consciousness, etc. The union of the object, the door or sense faculty, and the consciousness is called "contact" (phassa). There can be no awareness without contact. For contact to occur all three components must be present — object, door, and consciousness. If one is missing there will be no contact. The process of the arising of consciousness and the subsequent train of events is analyzed in detail in the Abhidhamma. A study of this analysis will show that only "bare phenomena" are taking place and that there is no "self" involved in this process. This is the no-self characteristic of existence.

As a computer scientist you are bringing some baggage with you that will continue to get in the way of what you want to find in the Dharma. I am speaking from the perspective of a computer scientist that spent thirty years looking into the same questions you are asking, ultimately finding the answers in contemplative practice.

While consciousness is categorized in the Dharma in ways that may have led you to believe that consciousness is some thing that exists separate and apart from its cognitive contents, reaching out to contact that content, the actual structure, which you can discover first-hand through meditative practices (today’s mindfulness meditation being the first baby-step on the path) is the inverse of what you believe it to be.

For me, the ultimate roadblock on the path you are following was explaining human creativity (rather than explaining it away), because, upon analysis, the proposed solutions to explaining it always assumed the result, and thus were never more than magical thinking. An example is the foundational belief, found widespread in many fields of knowledge, that order arises randomly—and sticks around—without some organizing principle driving it. That’s magical thinking.

Consciousness of some object being taken as a structure of real things harboring a ghost in the machine that somehow imparts a new feature onto its dull matter, no matter how subtly the mechanism is crafted, must assume as a given, the ability to know, be aware, or be cognizant of those skandas you’ve read about. It’s not to be found in dull matter, so you have to turn the problem around.

If you want a textual reference to an in-depth treatment of mind, and specifically “where is mind?” I highly recommend the Surangama Sutra, also known as The Sutra of Heroic Progress. There are three extant English translations of it, with my favorite being the Goddard translation because of it’s conciseness (repeating material being skipped), and the lengths gone to by the translators and the editor, Goddard, to not use unfamiliar terminology.