You shouldn't walk away from a problem. Too many individuals find that the anger situation becomes uncomfortable. However, the consequences of sweeping it under the rug are far more destructive than dealing with it at the moment. If things get too heated, agree to take that time out and vent your feelings during that time by writing them out. After the cooling down period, you will be more calm and honest in your argument.
Arguments are normal and healthy in relationships.
They actually bring people closer together and allow for a more intimate relationship. Resolving and surviving the conflict together will only serve to enhance and develop the relationship. Shutting down by using the silent treatment or pretending nothing is wrong will only build up and surface in greater distress next time around pulling you further apart each time. Learn to be objective. This does not mean to be cold or unfeeling, but rather a recognition that you and the person with whom you are angry are two separate individuals entitled to different needs and feelings.