Fully flexible, self-optimizing, digital hydraulic engines and methods with preheat

A method of operating a compression ignition engine comprising:

• taking air into a compression cylinder of the engine;
• compressing the air in the compression cylinder to raise the pressure and temperature of the air;
• passing the compressed air through a heat exchanger, and from the heat exchanger into a combustion cylinder during a compression stroke of the combustion cylinder by opening an air valve during the compression stroke of the combustion cylinder to allow the compressed air to pass from the heat exchanger into the combustion cylinder, and subsequently closing the air valve during the compression stroke of the combustion cylinder to stop the compressed air from passing from the heat exchanger into the combustion cylinder, thereby also preventing the compressed air from passing from the heat exchanger into the combustion cylinder during a power stroke of the combustion cylinder;
• further compressing the compressed air in the combustion cylinder during the compression stroke of the combustion cylinder;
• igniting fuel in the combustion cylinder at or after the end of the compression stroke by compression ignition, followed by the power stroke;
• opening an exhaust valve at the end of the power stroke and passing at least some of the exhaust in the combustion cylinder through the heat exchanger to heat air that has been compressed in the compression cylinder and is then passing through the heat exchanger.